Amortised resource analysis with separation logic

Type-based amortised resource analysis following Hofmann and Jost—where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline—have been successful in providing concrete resource bounds for functional programs, with good support for inference. In this work we translate the idea of amortised resource analysis to imperative languages by embedding a logic of resources, based on Bunched Implications, within Separation Logic. The Separation Logic component allows us to assert the presence and shape of mutable data structures on the heap, while the resource component allows us to state the resources associated with each member of the structure. We present the logic on a small imperative language with procedures and mutable heap, based on Java bytecode. We have formalised the logic within the Coq proof assistant and extracted a certified verification condition generator. We demonstrate the logic on some examples, including proving termination of in-place list reversal on lists with cyclic tails

Looking Forward Transdisciplinary Modeling, Environmental Forecasting, and Management

In the 1970s, the International Decade of Ocean Exploration (IDOE) set the stage for an era of global ocean research programs (NRC, 1999). Although scientists had long explored the "seven seas," it was only in the late 1960s that observing the ocean at synoptic scales became feasible. This capability, together with the lessons learned from IDOE, allowed for the growth of major oceanographic initiatives. In particular, the late 1980s and the 1990s marked two decades of large oceanographic programs, two of which, the World Ocean Circulation Experiment (WOCE; http://www.nodc.noaa.gov/woce/wdiu/wocedocs/index.htm#design), and the Joint Global Ocean Flux Study (JGOFS; http://www1.whoi.edu), resulted in important advances and transformations in ocean research that fostered the subsequent development of the Global Ocean Ecosystem Dynamics program (GLOBEC; http://www.globec.org)

Proton Decay from Excited States in Spherical Nuclei

Based on a single particle model which describes the time evolution of the wave function during tunneling across a one dimensional potential barrier we study the proton decay of $^{208}$Pb from excited states with non-vanishing angular momentum $\ell$. Several quantities of interest in this process like the decay rate $\lambda$, the period of oscillation $T_{osc}$, the transient time $t_{tr}$, the tunneling time $t_{tun}$ and the average value of the proton packet position $r_{av}$ are computed and compared with the WKB results.Comment: 12 pages, 4 figure

Modeling Oyster Populations. IV. Rates of Mortality, Population Crashes, and Management

A time-dependent energy-flow model was used to examine how mortality affects oyster populations over the latitudinal gradient from Galveston Bay, Texas, to Chesapeake Bay, Virginia. Simulations using different mortality rates showed that mortality is required for market-site oysters to be a component of the population\u27s size-frequency distribution; otherwise a population of stunted individuals results. As mortality extends into the juvenile sizes, the population\u27s size frequency shifts toward the larger sizes. In many cases adults increase despite a decrease in overall population abundance. Simulations, in which the timing of mortality varied, showed that oyster populations are more susceptible to population declines when mortality is restricted to the summer months. Much higher rates of winter mortality can be sustained. Comparison of simulations of Galveston Bay and Chesapeake Bay showed that oyster populations are more susceptible to intense population declines at higher latitudes. The association of population declines with disease agents causing summer mortality and the increased frequency of long-term declines at high latitudes result from the basic physiology of the oyster and its population dynamics cycle. Accordingly, management decisions on size limits, seasons and densities triggering early closure must differ across the latitudinal gradient and in populations experiencing different degrees of summer and winter mortality relative to their recruitment rate. More flexible size limits might be an important management tool. When fishing is the primary cause of mortality, populations should be managed more conservatively in the summer. The latitudinal gradient in resistance to mortality requires more conservative management at higher latitudes and different management philosophies from those used in the Gulf of Mexico

Environmental Effects on the Growth and Development of Eastern Oyster, Crassostrea virginica (Gmelin, 1791), Larvae: A Modeling Study

The effects of temperature, food concentration, salinity and turbidity on the growth and development of Crassostrea virginica larvae were investigated with a time-dependent mathematical model. Formulations used in the model for larval growth are based upon laboratory data. Simulations were done using temperature conditions characteristic of Laguna Madre, Galveston Bay, Apalachicola Bay, North Inlet and Chesapeake Bay. These simulations show that the duration of the planktonic larval phase, which is determined by larval growth rate, decreases at lower latitudes in response to warmer water temperatures. Also, oysters in the more southern locations have a longer spawning season during which the oyster population can produce more larvae. Simulations were done for Galveston Bay and Chesapeake Bay using idealized time series of food supply that included higher concentrations in the spring, summer or fall. Additional simulations considered the effects of increased food supply in both spring and fall seasons. The results show that shifting the period of enhanced food supply from March-April to April-May, when temperatures are warmer, reduces the minimum larval planktonic period from 44 to 34 days. Shifting the fall bloom from August-September to September-October, however, does not appreciably change the minimum larval planktonic period. The final set of simulations considered the effect of low salinity events and turbidity on the planktonic period of the larvae of Crassostrea virginica. By imposing a simulated low salinity (5 ppt) event of one month duration in August, the larval planktonic time is increased by about 39% over normal August salinities. Turbidity concentrations less than 0.1 g l-1 result in slightly decreased planktonic times. These model results show clearly the importance of ambient environmental conditions in determining the planktonic time of larvae of Crassostrea virginica, and hence their ultimate recruitment to the adult oyster population

Modeling Diseased Oyster Populations. II. Triggering Mechanisms for Perkinsus marinus Epizootics

Densities of Crassostrea virginica remain high enough to support substantial fisheries throughout the Gulf of Mexico despite high mortality rates produced by the endoparasite Perkinsus marinus. The infrequency of epizootics in these populations suggests that controls exist on the disease intensification process. The progression of epizootics in oyster populations, the factors that trigger epizootics, and the factors that terminate epizootics once started were investigated with a coupled oyster population—P. marinus model. The time development of a simulated epizootic was triggered by environmental conditions that occurred and disappeared as much as t8 months prior to the onset of mortality in the oyster population. Initiation of epizootic conditions was detected as an increase in infection intensities in the submarket-size adult and juvenile portions of the oyster population. Infection intensity of the market-size adults is maintained at a relatively stable level by the death of heavily infected individuals and the slow rate of P. marinus division at high infection intensities. Once started, most of the simulated epizootics resulted in population extinction in 2 to 4 years. Stopping an epizootic required reducing the infection intensity in the submarket-size adults and juveniles. The infection intensity of market-size adults does not need to be reduced to stop an epizootic nor must it be raised to start one. The simulated oyster populations show that a reduction in ingestion rate (by reduced food supply or increased turbidity) can trigger an epizootic, especially if the reduction occurs during the summer. lncreasing food supply or decreasing turbidity in the following year does not necessarily prevent the occurrence of an epizootic. Rather, the onset or the event is simply delayed. Additional simulations show that the relative combination of variations in salinity and temperature is important in determining the occurrence of an epizootic. A dry (high-salinity) summer followed by a warm winter produces conditions that favor the development of an epizootic. Conversely, a warm dry year followed by a cool wet year fails to produce an epizootic. Simulations that consider variations in the biological characteristics of oyster populations, such as changes in recruitment rate or disease resistance, show that these are important in regulating the occurrence of an epizootic as well as in terminating the event. In particular, increased recruitment rate dilutes the infected population sufficiently to terminate an epizootic. One primary conclusion that can be obtained from these simulations is that epizootics of P. marinus in oyster populations are difficult to generate simply with changes in either temperature or salinity. Rather, the epizootics are triggered by some other factor, such as reduced food supply or reduced recruitment rate, that occurs prior to or coincident with high salinity or temperature conditions

Population Dynamics Model of the Hard Clam, Mercenaria Mercenaria: Development of the Age- and Length-Frequency Structure of the Population

An individual-based model was developed to simulate growth of the hard clam, Mercenaria mercenaria, in response to temperature, salinity and food supply conditions. Unique characteristics of the model are that: (1) length and tissue weight are related only by condition index, so that weight, up to a point, can vary independently of length, and (2) age is decoupled from length. Tissue weight changes result from the difference in assimilation and respiration. Changes in hard clam condition are determined from a standard length-weight relationship for average hard clam growth. Changes in hard clam length (growth) occur only when condition index is greater than zero, which happens when excess weight for a given length is attained. No change in length occurs if condition index is zero (mean case) or negative (less weight than expected at a given length). This model structure resolves limitations that accompany models used to simulate the growth and development of shellfish populations. The length-frequency distribution for a cohort was developed from the individual-based model through simulation of a suite of genotypes with varying physiological capabilities. Hard clam populations were then formed by the yearly concatenation of cohorts with partially independent trajectories that are produced by cohort- and population-based processes. Development and verification of the hard clam model was done using long-term data sets from Great South Bay, New York that have been collected by the Town of Islip, New York. The ability to separately track length and age in the simulations allowed derivation of a general mathematical relationship for describing age-length relationships in hard clam populations. The mathematical relationship, which is based on a twisted bivariate Gaussian distribution, reproduces the features of age-length distributions observed for hard clam populations. The parameters obtained from fitting the twisted bivariate Gaussian to simulated hard clam length-frequency distributions obtained for varying conditions yield insight into the growth and mortality processes and population-dependent processes, compensatory and otherwise, that structured the population. This in turn provides a basis for development of theoretical models of population age-length compositions. The twisted bivariate Gaussian also offers the possibility of rapidly and inexpensively developing age-length keys, used to convert length-based data to age-based data, by permitting a relatively few known age-length pairs to be expanded into the full age- and length-frequency structure of the population

Effects of the Fishery on the Northern Quahog (=Hard Clam, Mercenaria Mercenaria L.) Population in Great South Bay, New York: A Modeling Study

A numerical bioenergetics simulation model based on the physiological processes affecting individual clams across a range of phenotypes describing a cohort has been developed and applied to the conditions in Great South Bay, New York. The clam population is relatively sensitive to food and to a lesser extent to temperature within this system. The timing of temperature and food in tire spring, and more importantly in the fall, call increase population sensitivity beyond the effects of one factor operating alone. The effects of fishing on the stocks in proportion to the size structure present. and as directed fisheries oil various size classes (littleneck, cherrystone, chowder) was stimulated. Recruitment overfishing was responsible for the stock decline in the 1970s and 1980s, but the continued decline into the late 1990s and 2000s cannot be attributed to fishing alone. Recruit-per-adult declined after the mid 1990s. Modeled stock recovery times Under constant environmental conditions are oil order of 10-15 or more years depending oil the exploitation rate, Under base conditions a proportional fishery that removes approximately 25% of the stock, or a littleneck fishery that removes approxmately, 37.5% of that size class annually Would provide the best economic returns underconstant average environmental conditions. Slightly less harvest Would be desirable to avoid overfishing ill years of less than optimal environmental conditions

Modeling Oyster Populations II. Adult Size and Reproductive Effort

A time-dependent model of energy flow in post-settlement oyster populations is used to examine the factors that influence adult size and reproductive effort in a particular habitat, Galveston Bay, Texas, and in habitats that extend from Laguna Madre, Texas to Chesapeake Bay. The simulated populations show that adult size and reproductive effort are determined by the allocation of net production to somatic or reproductive tissue development and the rate of food acquisition, both of which are temperature dependent. For similar food conditions, increased temperature reduces the allocation of net production to somatic tissue and increases the rate of food acquisition. This temperature effect, however, is mediated by changes in food supply. Within the Gulf of Mexico, oyster size declines from north to south because increased temperature decreases the allocation of net production to somatic growth. An increase in food supply generally results in increased size as more energy is used in somatic growth; however, at low latitudes, as food supply increases, adult size decreases because the allocation of more net production to reproduction outweighs the effect of increased rates of food acquisition. Variations in temperature and food supply affect reproductive effort more than adult size because the rate of energy flow through the oyster is higher in warmer months when most net production is allocated to reproduction and small changes in temperature substantially change the spawning season. The wide range of reproductive effort expected from small changes in temperature and food supply suggest that comparisons of adult size and reproductive effort between oyster populations can only be made within the context of a complete environmental analysis of food supply and associated physical parameters and an energy flow model