Abstract:
The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each promoter might vary in DNA sequence relative to the average consensus. Here we examine the linguistic organization of gene promoter networks, wherein each node in the network represents a promoter and links between nodes represent the extent of base pair-sharing. Prior work revealed a fractal nucleus in several σ-factor regulons from Escherichia coli. We extend these findings to show fractal nuclei in gene promoter networks from three bacterial species, E. coli, Bacillus subtilis, and Pseudomonas aeruginosa. We surveyed several non-σ transcription factors from these species and found that many contain a nucleus that is both visually and numerically fractal. Promoter footprint size scaled as a negative power-law with both information entropy and fractal dimension, while the latter two parameters scaled positively and linearly. The fractal dimension of the diffuse networks (dB = ~1.7) was close to that expected of a diffusion limited aggregation process, confirming prior predictions as to a possible mechanism for development of this structure.

Abstract:
Much is known regarding the structure and logic of genetic regulatory networks. Less understood is the contextual organization of promoter signals used during transcription initiation, the most pivotal stage during gene expression. Here we show that promoter networks organize spontaneously at a dimension between the 1-dimension of the DNA and 3-dimension of the cell. Network methods were used to visualize the global structure of E. coli sigma (σ) recognition footprints using published promoter sequences (RegulonDB). Footprints were rendered as networks with weighted edges representing bp-sharing between promoters (nodes). Serial thresholding revealed phase transitions at positions predicted by percolation theory, and nuclei denoting short steps through promoter space with geometrically constrained linkages. The network nuclei are fractals, a power-law organization not yet described for promoters. Genome-wide promoter abundance also scaled as a power-law. We propose a general model for the development of a fractal nucleus in a transcriptional grammar.

Abstract:
Aim: To analyse whether there are changes in sodium and potassium serum levels during chronic treatment with the diphenyl methanes bisacodyl and sodium picosulfate. Methods: A literature search was done using PubMed, and the reference lists of pertinent papers were screened for additional studies. Only studies of at least 4 weeks duration were considered for further analysis. Results: Four relevant studies were identified. In three randomised controlled trials with 5 to 10 mg daily of bisacodyl or sodium picosulfate, respectively, over four weeks no electrolyte losses were found. Hypokalemia was also not a problem in a group of patients with paraplegia using bisacodyl suppositories for 2 to 34 years. Conclusions: Electrolyte losses, particularly hypokalemia, are not a problem when bisacodyl or sodium picosulfate are used long-term.

Abstract:
We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density.

Background: Our aim was to investigate the frequency of elevated liver enzymes and NAFLD in patients with known insulin resistance during 15 years of follow-up. Methods: Subjects with insulin resistance were identified from a population-based prospective cohort study in Sweden, Malm? Diet and Cancer Study, conducted in 1991-1996. Inall, 285 non-diabetic subjects with insulin resistance established by HOMA-IR (homeostasis model assessment) were invited to do the liver function testing and if elevated, they should be further assessed by radiological examination of the liver, anthropometric measures and blood testing. Results: 165 subjects (57.9%) agreed to do the liver function testing. Of these, 25 subjects (15%) had elevated liver enzymes. After exclusion of other diseases, 5 of the remaining 21 subjects (23.8%) had radiological signs of steatosis. Liver steatosis significantly correlated with ALT (alanine aminotransferase) (p = 0.04), HOMA-IR (p = 0.00) and the metabolic syndrome (p = 0.03). 80% of the subjects with NAFLD had either developed type 2 diabetes mellitus or had impaired fasting glucose and 80% fulfilled the WHO-criteria for the metabolic syndrome, which were of significant differences to the group without NAFLD. Conclusion: The risk of developing elevated liver enzymes and NAFLD at long-term follow-up in insulin resistant subjects is not insignificant, but mainly associated with the simultaneous development of impaired fasting glucose, established diabetes mellitus and/ or the metabolic syndrome.

Abstract:
Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation.The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 – 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease.The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditio

Abstract:
Let a family of gradient Gaussian vector fields on $ \mathbb{Z}^d $ be given. We show the existence of a uniform finite range decomposition of the corresponding covariance operators, that is, the covariance operator can be written as a sum of covariance operators whose kernels are supported within cubes of diameters $ \sim L^k $. In addition we prove natural regularity for the subcovariance operators and we obtain regularity bounds as we vary within the given family of gradient Gaussian measures.

Abstract:
The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as e.g. wind or solar) via a market mechanism, namely by variable power prices that adapt demand to supply. The standard model of an average economic agent predicts that fluctuations are reduced by such an adaptive pricing mechanism. However, the underlying assumption that the actions of all agents average out on the time axis is not always true in a market of many agents. We numerically study an econophysics agent model of an adaptive power market that does not assume averaging a priori. We find that when agents are exposed to source noise via correlated price fluctuations (as adaptive pricing schemes suggest), the market may amplify those fluctuations. In particular, small price changes may translate to large load fluctuations through catastrophic consumer synchronization. As a result, an adaptive power market may cause the opposite effect than intended: Power fluctuations are not dampened but amplified instead.

Abstract:
We consider the problem of minimizing a convex separable logarithmic function over a region defined by a convex inequality constraint or linear equality constraint, and two-sided bounds on the variables (box constraints). Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems such as problems of production planning and scheduling, allocation of resources, decision making, facility location problems, and so forth. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.

Abstract:
We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.