Preliminary Investigation on the Physiology and Ecology of Luminescence in the Copepod, Metridia lucens

1. Skin glands believed to be the source of luminescence were found on the anterior portion of the head, on the last thoracic segment, and on the posterior margins of each segment of the abdomen. 2. The maximum intensity of the luminescent flash was 1.2 x 10-3 µw./cm.2 (at 18 cm.). The flash rose rapidly to peak intensity and then decayed slowly. The total duration of the flashes with peaks greater than 10-4 µw./cm.2 ranged from 3 to 50 seconds. 3. The peak of the luminescence spectrum occcurred at 482 mµ and the curve fell off to one-half the maximum value at 440 mµ and 525 mµ. 4. The ability of Metridia to luminesce on stimulation was found to be largely unaffected by prolonged laboratory culture. Starvation had little effect on the luminescence for the first three weeks and there was never any inhibition by previous light- or dark-adaptation. 5. With an increase in the strength of the electric stimulus from 0.3 amp. to 0.7 amp., the intensity of the luminescent flash was found to increase. With pulses stronger than 0.7 amp. no change in intensity was recorded but the number of successive responses to repeated stimuli was reduced. Duration of the pulse had little effect on the intensity or the number of successive responses. 6. Metridia showed a lag time of 8-10 msc. to the beginning of the luminescent response. The lag time to the peak of the luminescent response varied from 20 to 60 msc. 7. There was no spontaneous luminescence produced by groups of Metridia under conditions of constant darkness. However, the presence of certain planktonic predators, most notably Meganyctiphanes norvegica, caused a brilliant display of luminescence. The number of flashes attributable to Metridia was always greater than the number of Metridia eaten by the predator. There was little evidence that the luminescent euphausiid, Meganyctiphanes, flashed spontaneously either in the presence or absence of its prey. 8. Observations on the behavior of Metridia during and just after luminescence suggest that the flashing may be involved in an escape mechanism, but the precise effect of the light on the predator has not been determined

The Work-Hamiltonian Connection and the Usefulness of the Jarzynski Equality for Free Energy Calculations

The connection between work and changes in the Hamiltonian for a system with a time-dependent Hamiltonian has recently been called into question, casting doubt on the usefulness of the Jarzynski equality for calculating free energy changes. In this paper, we discuss the relationship between two possible definitions of free energy and show how some recent disagreements regarding the applicability of the Jarzynski equality are the result of different authors using different definitions of free energy. Finally, in light of the recently raised doubts, we explicitly demonstrate that it is indeed possible to obtain physically relevant free energy profiles from molecular pulling experiments by using the Jarzynski equality and the results of Hummer and Szabo.Comment: 3 page

Solutions of Backward Stochastic Differential Equations on Markov Chains

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200

Channel assignment in cellular radio

Some heuristic channel-assignment algorithms for cellular systems are described. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel-assignment problem can be viewed as a generalized graph-coloring problem, and these algorithms have been developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms. The channel-assignment problem is formulated as a minimum-span problem, i.e. a problem wherein the requirement is to find the minimum bandwidth necessary to satisfy a given demand. Examples are presented, and algorithm performance results are discussed

Filters and smoothers for self-exciting Markov modulated counting processes

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework

Performance limits for channelized cellular telephone systems

Studies the performance of channel assignment algorithms for “channelized” (e.g., FDMA or TDMA) cellular telephone systems, via mathematical models, each of which is characterized by a pair (H,p), where H is a hypergraph describing the channel reuse restrictions, and p is a probability vector describing the variation of traffic intensity from cell to cell. For a given channel assignment algorithm, the authors define T(r) to be the amount of carried traffic, as a function of the offered traffic, where both r and T(r) are measured in Erlangs per channel. They show that for a given H and p, there exists a function TH,p(r), which can be computed by linear programming, such that for every channel assignment algorithm, T(r) ≤ TH,p(r). Moreover, they show that there exist channel assignment algorithms whose performance approaches TH,p (r) arbitrarily closely as the number of channels increases. As a corollary, they show that for a given (H,p) there is a number r0 , which also can be computed by linear programming, such that if the offered traffic exceeds r0, then for any channel assignment algorithm, a positive fraction of all call requests must be blocked, whereas if the offered traffic is less than r0, all call requests can be honored, if the number of channels is sufficiently large. The authors call r0, whose units are Erlangs per channel, the capacity of the cellular system

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.Comment: Published in at http://dx.doi.org/10.1214/09-AAP619 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Arthropods Associated With Purple Loosestrife in Illinois Wetlands

We estimated and described the arthropod fauna on purple loosestrife (Lythrum salicaria) plants in northeastern Illinois wetlands. A total of 1063 individual arthropods were collected—930 insects and 133 arachnids. The av- erage number of arthropods ranged from 19.00 to 86.75 individuals per loos- estrife plants of a single root crown. We collected individuals from twenty-five families representing 8 orders of insects. Miridae, Anthocoridae, Lygaeidae, Cicadellidae, and Aphididae were each represented by at least 50 individuals. Three orders and ten families were found that had not been previously reported as occurring on purple loosestrife, but many of these taxa were represented by only a few individuals