Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System

Juvenile salmonid distribution, growth, condition, origin, and environmental and species associations in the Northern California Current

Information is summarized on juvenile salmonid distribution, size, condition, growth, stock origin, and species and environmental associations from June and August 2000 GLOBEC cruises with particular emphasis on differences related to the regions north and south of Cape Blanco off Southern Oregon. Juvenile salmon were more abundant during the August cruise as compared to the June cruise and were mainly distributed northward from Cape Blanco. There were distinct differences in distribution patterns between salmon species: chinook salmon were found close inshore in cooler water all along the coast and coho salmon were rarely found south of Cape Blanco. Distance offshore and temperature were the dominant explanatory variables related to coho and chinook salmon distribution. The nekton assemblages differed significantly between cruises. The June cruise was dominated by juvenile rockfishes, rex sole, and sablefish, which were almost completely absent in August. The forage fish community during June comprised Pacific herring and whitebait smelt north of Cape Blanco and surf smelt south of Cape Blanco. The fish community in August was dominated by Pacific sardines and highly migratory pelagic species. Estimated growth rates of juvenile coho salmon were higher in the GLOBEC study area than in areas farther north. An unusually high percentage of coho salmon in the study area were precocious males. Significant differences in growth and condition of juvenile coho salmon indicated different oceanographic environments north and south of Cape Blanco. The condition index was higher in juvenile coho salmon to the north but no significant differences were found for yearling chinook salmon. Genetic mixed stock analysis indicated that during June, most of the Chinook salmon in our sample originated from rivers along the central coast of Oregon. In August, chinook salmon sampled south of Cape Blanco were largely from southern Oregon and northern California; whereas most chinook salmon north of Cape Blanco were from the Central Valley in California

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

Hydrogeologic controls on ground-water and contaminant discharge to the Columbia River near the Hanford Townsite

The purpose of this study is to quantify ground-water and contaminant discharge to the Columbia River in the Hanford Townsite vicinity. The primary objectives of the work are to: describe the hydrogeologic setting and controls on ground-water movement and contaminant discharge to the Columbia River; understand the river/aquifer relationship and its effects on contaminant discharge to the Columbia River; quantify the ground-water and contaminant mass discharge to the Columbia River; and provide data that may be useful for a three-dimensional model of ground-water flow and contaminant transport in the Hanford Townsite study area. The majority of ground-water contamination occurs within the unconfined aquifer; therefore, ground-water and contaminant discharge from the unconfined aquifer is the emphasis of this study. The period of study is primarily from June 1990 through March 1992

Spatial and trophic overlap of marked and unmarked Columbia River Basin spring Chinook salmon during early marine residence with implications for competition between hatchery and naturally produced fish

Ecological interactions between natural and hatchery juvenile salmon during their early marine residence, a time of high mortality, have received little attention. These interactions may negatively influence survival and hamper the ability of natural populations to recover. We examined the spatial distributions and size differences of both marked (hatchery) and unmarked (a high proportion of which are natural) juvenile Chinook salmon in the coastal waters of Oregon andWashington from May to June 1999–2009. We also explored potential trophic interactions and growth differences between unmarked and marked salmon. Overlap in spatial distribution between these groups was high, although catches of unmarked fish were low compared to those of marked hatchery salmon. Peak catches of hatchery fish occurred in May, while a prolonged migration of small unmarked salmon entered our study area toward the end of June. Hatchery salmon were consistently longer than unmarked Chinook salmon especially by June, but unmarked salmon had significantly greater body condition (based on length-weight residuals) for over half of the May sampling efforts. Both unmarked and marked fish ate similar types and amounts of prey for small (station) and large (month, year) scale comparisons, and feeding intensity and growth were not significantly different between the two groups. There were synchronous interannual fluctuations in catch, length, body condition, feeding intensity, and growth between unmarked and hatchery fish, suggesting that both groups were responding similarly to ocean conditions.Keywords: Wild, Competition, Spatial, Marine, Hatchery, Columbia River Basin, Juvenile Chinook salmon, Trophi

Computation of Lyapunov functions for systems with multiple attractors

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapunov function is interpolated over the simplices of a simplicial complex and, by checking certain inequalities at the vertices of the complex, we can identify the region in which the Lyapunov function is decreasing along system trajectories. The resulting Lyapunov function gives information on the qualitative behavior of the dynamics, including lower bounds on the basins of attraction of the individual local attractors. We develop the theory in detail and present numerical examples demonstrating the applicability of our method

Early Ocean Dispersal Patterns of Columbia River Chinook and Coho Salmon

Several evolutionarily significant units (ESUs) of Columbia River basin Chinook Salmon Oncorhynchus tshawytscha and Coho Salmon O. kisutch are listed as threatened or endangered under the U.S. Endangered Species Act. Yet little is known about the spatial and temporal distributions of these ESUs immediately following ocean entry, when year-class success may be determined. We documented differences in dispersal patterns during the early ocean period among groups defined by ESU, adult run timing, and smolt age. Between 1995 and 2006, 1,896 coded-wire-tagged juvenile fish from the Columbia River basin were recovered during 6,142 research trawl events along the West Coast of North America. Three distinct ocean dispersal patterns were observed: (1) age-1 (yearling) mid and upper Columbia River spring-run and Snake River spring–summer-run Chinook Salmon migrated rapidly northward and by late summer were not found south of Vancouver Island; (2) age-0 (subyearling) lower Columbia River fall, upper Columbia River summer, upper Columbia River fall, and Snake River fall Chinook Salmon dispersed slowly, remaining mainly south of Vancouver Island through autumn; and (3) age-1 lower Columbia River spring, upper Columbia River summer, and upper Willamette River spring Chinook Salmon and Coho Salmon were widespread along the coast from summer through fall, indicating a diversity of dispersal rates. Generally, the ocean dispersal of age-1 fish was faster and more extensive than that of age-0 fish, with some age-1 fish migrating as fast as 10–40 km/d (0.5–3.0 body lengths/s). Within groups, interannual variation in dispersal was moderate. Identification of the distinct temporal and spatial ocean distribution patterns of juvenile salmon from Columbia River basin ESUs is important in order to evaluate the potential influence of changing ocean conditions on the survival and long term sustainability of these fish populations

Initiation of V(D)J Recombination by Dβ-Associated Recombination Signal Sequences: A Critical Control Point in TCRβ Gene Assembly

T cell receptor (TCR) β gene assembly by V(D)J recombination proceeds via successive Dβ-to-Jβ and Vβ-to-DJβ rearrangements. This two-step process is enforced by a constraint, termed beyond (B)12/23, which prohibits direct Vβ-to-Jβ rearrangements. However the B12/23 restriction does not explain the order of TCRβ assembly for which the regulation remains an unresolved issue. The initiation of V(D)J recombination consists of the introduction of single-strand DNA nicks at recombination signal sequences (RSSs) containing a 12 base-pairs spacer. An RSS containing a 23 base-pairs spacer is then captured to form a 12/23 RSSs synapse leading to coupled DNA cleavage. Herein, we probed RSS nicks at the TCRβ locus and found that nicks were only detectable at Dβ-associated RSSs. This pattern implies that Dβ 12RSS and, unexpectedly, Dβ 23RSS initiate V(D)J recombination and capture their respective Vβ or Jβ RSS partner. Using both in vitro and in vivo assays, we further demonstrate that the Dβ1 23RSS impedes cleavage at the adjacent Dβ1 12RSS and consequently Vβ-to-Dβ1 rearrangement first requires the Dβ1 23RSS excision. Altogether, our results provide the molecular explanation to the B12/23 constraint and also uncover a ‘Dβ1 23RSS-mediated’ restriction operating beyond chromatin accessibility, which directs Dβ1 ordered rearrangements

Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function