scholarly journals Equilibrium distributions of physical clusters

1975 ◽  
Vol 45 (3) ◽  
pp. 233-246 ◽  
Author(s):  
Michael G. Mürmann
Keyword(s):  
Equilibrium Distributions ◽  
Physical Clusters

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

scholarly journals Dynamics of Microsatellite Divergence Under Stepwise Mutation and Proportional Slippage/Point Mutation Models

Genetics ◽  
2001 ◽  
Vol 159 (2) ◽  
pp. 839-852 ◽  
Author(s):  
Peter P Calabrese ◽  
Richard T Durrett ◽  
Charles F Aquadro
Keyword(s):  
Point Mutations ◽  
Genetic Distances ◽  
Mutational Bias ◽  
Human Populations ◽  
Mutation Model ◽  
Perfect Repeat ◽  
Stepwise Mutation ◽  
Equilibrium Distributions ◽  
Theoretical Results ◽  
Polymerase Slippage

Abstract Recently Kruglyak, Durrett, Schug, and Aquadro showed that microsatellite equilibrium distributions can result from a balance between polymerase slippage and point mutations. Here, we introduce an elaboration of their model that keeps track of all parts of a perfect repeat and a simplification that ignores point mutations. We develop a detailed mathematical theory for these models that exhibits properties of microsatellite distributions, such as positive skewness of allele lengths, that are consistent with data but are inconsistent with the predictions of the stepwise mutation model. We use our theoretical results to analyze the successes and failures of the genetic distances (δμ)2 and DSW when used to date four divergences: African vs. non-African human populations, humans vs. chimpanzees, Drosophila melanogaster vs. D. simulans, and sheep vs. cattle. The influence of point mutations explains some of the problems with the last two examples, as does the fact that these genetic distances have large stochastic variance. However, we find that these two features are not enough to explain the problems of dating the human-chimpanzee split. One possible explanation of this phenomenon is that long microsatellites have a mutational bias that favors contractions over expansions.

Transmembrane Activity Gradients of K and cl in the Muscle Fibres of Osmoconforming Marine Decapod Crustaceans

1978 ◽  
Vol 72 (1) ◽  
pp. 127-140
Author(s):  
ROBERT W. FREEL
Keyword(s):  
Sea Water ◽  
Membrane Potentials ◽  
Resting Potential ◽  
Muscle Fibres ◽  
Salinity Adaptation ◽  
Decapod Crustaceans ◽  
Marine Crustaceans ◽  
Equilibrium Distributions

1. The resting membrane potentials (Em) and the transmembrane activity gradients for K and Cl were measured in the muscle fibres of osmoconforming (Callianassa and Cancer) and weakly osmoregulating (Pachygrapsus) marine crustaceans acclimated to various osmotic conditions. 2. The muscle membranes of sea water acclimated crabs behave as good K electrodes. However, a slight contribution of Na to the resting potential was demonstrated in all species. The ratio PNa/PK was about 0.01. Equilibrium potentials (measured with ion-selective microelectrodes) for Cl were equal to Em, while EK was always more negative than Em as a result of the slight Na contribution. 3. Acclimation to dilute or concentrated sea water had little effect on the K electrode properties or Na permeabilities of these fibres. The muscle fibres were depolarized in crabs acclimated to concentrated sea water and were hyperpolarized in crabs adapted to dilute sea water. These changes resulted solely from alterations in (aK)i/ (aK)O which were in turn brought about by changes in cellular and haemolymph hydration. 4. Since the Na contribution to Em was so small in all conditions, it was concluded that the distributions of K and Cl are best considered in terms of Donnan equilibria, and that the cellular K and Cl adjustments observed during salinity adaptation reflect the passive re-establishment of new equilibrium distributions for these ions.

scholarly journals EQUILIBRIUM ASSET RETURNS IN FINANCIAL MARKETS

2019 ◽  
Vol 22 (02) ◽  
pp. 1850063 ◽  
Author(s):  
DILIP B. MADAN ◽  
WIM SCHOUTENS
Keyword(s):  
Financial Markets ◽  
Fixed Points ◽  
Asset Prices ◽  
Asset Returns ◽  
Expected Returns ◽  
Response Functions ◽  
Limit Laws ◽  
Return Distributions ◽  
Equilibrium Distributions ◽  
The Cost

Return distributions in the class of pure jump limit laws are observed to reflect numerous asymmetries between the upward and downward motions of asset prices. The return distributions are modeled by self-decomposable parametric laws with all parameters continuously responding to each other. Fixed points of the response functions define equilibrium distributions. The equilibrium distributions that can arise in practice are constrained by the level of return acceptability they may attain. As a consequence, expected returns are equated to risk measured by the cost of purchasing the negative of the centered return. The asymmetries studied include differences in scale, speed, power variation, excitation and cross-excitation.

Sign in / Sign up

Export Citation Format

Share Document