Method for finding metabolic properties based on the general growth law. Liver examples. A General framework for biological modeling

We propose a method for finding metabolic parameters of cells, organs and whole organisms, which is based on the earlier discovered general growth law. Based on the obtained results and analysis of available biological models, we propose a general framework for modeling biological phenomena and discuss how it can be used in Virtual Liver Network project. The foundational idea of the study is that growth of cells, organs, systems and whole organisms, besides biomolecular machinery, is influenced by biophysical mechanisms acting at different scale levels. In particular, the general growth law uniquely defines distribution of nutritional resources between maintenance needs and biomass synthesis at each phase of growth and at each scale level. We exemplify the approach considering metabolic properties of growing human and dog livers and liver transplants. A procedure for verification of obtained results has been introduced too. We found that two examined dogs have high metabolic rates consuming about 0.62 and 1 gram of nutrients per cubic centimeter of liver per day, and verified this using the proposed verification procedure. We also evaluated consumption rate of nutrients in human livers, determining it to be about 0.088 gram of nutrients per cubic centimeter of liver per day for males, and about 0.098 for females. This noticeable difference can be explained by evolutionary development, which required females to have greater liver processing capacity to support pregnancy. We also found how much nutrients go to biomass synthesis and maintenance at each phase of liver and liver transplant growth. Obtained results demonstrate that the proposed approach can be used for finding metabolic characteristics of cells, organs, and whole organisms, which can further serve as important inputs for many applications in biology (protein expression), biotechnology (synthesis of substances), and medicine.Comment: 20 pages, 6 figures, 4 table

Lower Bounds of Quantum Search for Extreme Point

We show that Durr-Hoyer's quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect answer for the functions with the single point of maximum chosen randomly with probability converging to 1. The lower bound as $\Omega (\sqrt{2^n /b})$ was established for the quantum search for solution of equations $f(x)=1$ where $f$ is a Boolean function with $b$ such solutions chosen at random with probability converging to 1.Comment: Some minor change

Equivalence is in the Eye of the Beholder

In a recent provocative paper, Lamport points out "the insubstantiality of processes" by proving the equivalence of two different decompositions of the same intuitive algorithm by means of temporal formulas. We point out that the correct equivalence of algorithms is itself in the eye of the beholder. We discuss a number of related issues and, in particular, whether algorithms can be proved equivalent directly.Comment: See also the ASM web site at http://www.eecs.umich.edu/gasm

Beaming effect from increased-index photonic crystal waveguides

We study the beaming effect of light for the case of increased-index photonic crystal (PhC) waveguides, formed through the omission of low-dielectric media in the waveguide region. We employ the finite-difference time-domain numerical method for characterizing the beaming effect and determining the mechanisms of loss and the overall efficiency of the directional emission. We find that, while this type of PhC waveguides is capable of producing a highly collimated emission as was demonstrated experimentally, the inherent characteristics of the structure result in a restrictively low efficiency in the coupling of light into the collimated beam of light.Comment: 4 pages, 5 figures, submitted to Applied Physics

On the dependence of X-ray burst rate on accretion and spin rate

Nuclear burning and its dependence on the mass accretion rate are fundamental ingredients for describing the complicated observational phenomenology of neutron stars in binary systems. Motivated by high quality burst rate data emerging from large statistical studies, we report general calculations relating bursting rate to mass accretion rate and neutron star rotation frequency. In this first work we neglect general relativistic effects and accretion topology, though we discuss where their inclusion should play a role. The relations we derive are suitable for different burning regimes and provide a direct link between parameters predicted by theory and what is to be expected in observations. We illustrate this for analytical relations of different unstable burning regimes that operate on the surface of an accreting neutron star. We also use the observed behaviour of burst rate to suggest new constraints on burning parameters. We are able to provide an explanation for the long standing problem of the observed decrease of burst rate with increasing mass accretion that follows naturally from these calculations: when accretion rate crosses a certain threshold, ignition moves away from its initially preferential site and this can cause a net reduction of the burst rate due to the effects of local conditions that set local differences in both burst rate and stabilization criteria. We show under which conditions this can happen even if locally the burst rate keeps increasing with accretion.Comment: Accepted for publication on Ap