Parabolic free boundary price formation models under market size fluctuations

In this paper we propose an extension of the Lasry-Lions price formation model which includes fluctuations of the numbers of buyers and vendors. We analyze the model in the case of deterministic and stochastic market size fluctuations and present results on the long time asymptotic behavior and numerical evidence and conjectures on periodic, almost periodic and stochastic fluctuations. The numerical simulations extend the theoretical statements and give further insights into price formation dynamics

Coherently controlled entanglement generation in a binary Bose-Einstein condensate

Considering a two-component Bose-Einstein condensate in a double-well potential, a method to generate a Bell state consisting of two spatially separated condensates is suggested. For repulsive interactions, the required tunnelling control is achieved numerically by varying the amplitude of a sinusoidal potential difference between the wells. Both numerical and analytical calculations reveal the emergence of a highly entangled mesoscopic state.Comment: 6 pages, 6 figures, epl2.cl

The developmental expression dynamics of Drosophila melanogaster transcription factors.

BACKGROUND: Site-specific transcription factors (TFs) are coordinators of developmental and physiological gene expression programs. Their binding to cis-regulatory modules of target genes mediates the precise cell- and context-specific activation and repression of genes. The expression of TFs should therefore reflect the core expression program of each cell. RESULTS: We studied the expression dynamics of about 750 TFs using the available genomics resources in Drosophila melanogaster. We find that 95% of these TFs are expressed at some point during embryonic development, with a peak roughly between 10 and 12 hours after egg laying, the core stages of organogenesis. We address the differential utilization of DNA-binding domains in different developmental programs systematically in a spatio-temporal context, and show that the zinc finger class of TFs is predominantly early expressed, while Homeobox TFs exhibit later expression in embryogenesis. CONCLUSIONS: Previous work, dissecting cis-regulatory modules during Drosophila development, suggests that TFs are deployed in groups acting in a cooperative manner. In contrast, we find that there is rapid exchange of co-expressed partners amongst the fly TFs, at rates similar to the genome-wide dynamics of co-expression clusters. This suggests there may also be a high level of combinatorial complexity of TFs at cis-regulatory modules.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Scaling property of the critical hopping parameters for the Bose-Hubbard model

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d > 1. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical parameters for d > 1 and any g with high accuracy.Comment: 5 pages, 5 figures. to appear in EPJ

A model of trophic flows in the northern Benguela upwelling system during the 1980s

A model of trophic flows through the northern Benguela between 1980 and 1989 was constructed using the ECOPATH approach. The model serves to close the temporal gap between models of the system for the 1970sand 1990s. The aim is to provide a workable model, with the intention of encouraging scientists working on different components of the ecosystem to collaborate to improve and update the model for more recent years.Ultimately, this type of model may form a basis for multispecies management approaches in the region. By the 1980s, sardine Sardinops sagax and hake Merluccius spp. stocks in the northern Benguela had both undergone a decline, yet were still heavily fished. Horse mackerel Trachurus trachurus capensis had increased over the previousdecade and was the dominant pelagic species during the 1980s, with high catches. Production by some groups, such as goby Sufflogobius bibarbatus, mesopelagic fish and demersal fish, was insufficient to sustainother components of the system. In all, 1.5 million tons of goby, 1.7 million tons of mesopelagic fish and 0.7 million tons of demersal fish (excluding hake) were required to support predators in the northern Benguela. Total biomass in the northern Benguela during the 1980s was high, comparable to that of the Peruvian system in the 1960s and almost double that of the northern Benguela during the 1970s. Horse mackerel and hake catches were both high, with fishing on hake being ecologically more expensive. Biomass of benthic producers, meioand macrobenthos were a quarter of the total biomass of these groups in the southern Benguela. The sensitivity of the model to parameter estimates is highlighted. Uncertainty about some of the parameters, thought to havemajor influences on the functioning of the model, is explored

Protein domain organisation: adding order.

BACKGROUND: Domains are the building blocks of proteins. During evolution, they have been duplicated, fused and recombined, to produce proteins with novel structures and functions. Structural and genome-scale studies have shown that pairs or groups of domains observed together in a protein are almost always found in only one N to C terminal order and are the result of a single recombination event that has been propagated by duplication of the multi-domain unit. Previous studies of domain organisation have used graph theory to represent the co-occurrence of domains within proteins. We build on this approach by adding directionality to the graphs and connecting nodes based on their relative order in the protein. Most of the time, the linear order of domains is conserved. However, using the directed graph representation we have identified non-linear features of domain organization that are over-represented in genomes. Recognising these patterns and unravelling how they have arisen may allow us to understand the functional relationships between domains and understand how the protein repertoire has evolved. RESULTS: We identify groups of domains that are not linearly conserved, but instead have been shuffled during evolution so that they occur in multiple different orders. We consider 192 genomes across all three kingdoms of life and use domain and protein annotation to understand their functional significance. To identify these features and assess their statistical significance, we represent the linear order of domains in proteins as a directed graph and apply graph theoretical methods. We describe two higher-order patterns of domain organisation: clusters and bi-directionally associated domain pairs and explore their functional importance and phylogenetic conservation. CONCLUSION: Taking into account the order of domains, we have derived a novel picture of global protein organization. We found that all genomes have a higher than expected degree of clustering and more domain pairs in forward and reverse orientation in different proteins relative to random graphs with identical degree distributions. While these features were statistically over-represented, they are still fairly rare. Looking in detail at the proteins involved, we found strong functional relationships within each cluster. In addition, the domains tended to be involved in protein-protein interaction and are able to function as independent structural units. A particularly striking example was the human Jak-STAT signalling pathway which makes use of a set of domains in a range of orders and orientations to provide nuanced signaling functionality. This illustrated the importance of functional and structural constraints (or lack thereof) on domain organisation.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Network growth models and genetic regulatory networks

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new links, allowing for the possibility that input and output links from a newly created node may have different probabilities of survival. We find some counterintuitive trends as parameters are varied, including the broadening of indegree distribution when the probability for retaining input links is decreased. We also find that both the scaling of transcription factors with genome size and the measured degree distributions for genes in yeast can be reproduced by the growth algorithm if and only if a special seed is used to initiate the process.Comment: 8 pages with 7 eps figures; uses revtex4. Added references, cleaner figure

Networks for all

A report on the Cold Spring Harbor Laboratory/Wellcome Trust conference on Network Biology, Hinxton, UK, 27-31 August 2008