Randomness in biology

Biology has contradictory relationships with randomness. First, it is a complex issue for an empirical science to ensure that apparently random events are truly random, this being further complicated by the loose definitions of unpredictability used in the discipline. Second, biology is made up of many different fields, which have different traditions and procedures for considering random events. Randomness is in many ways an inherent feature of evolutionary biology and genetics. Indeed, chance/Darwinian selection principles, as well as the combinatorial genetic lottery leading to gametes and fertilisation, rely, at least partially, on probabilistic laws that refer to random events. On the other hand, molecular biology has long been based on deterministic premises that have led to a focus on the precision of molecular interactions to explain phenotypes, and, consequently, to the relegation of randomness to the marginal status of ‘noise’. However, recent experimental results, as well as new theoretical frameworks, have challenged this view and may provide unifying explanations by acknowledging the intrinsic stochastic dimension of intracellular pathways as a biological parameter, rather than just as background noise. This should lead to a significant reappraisal of the status of randomness in the life sciences, and have important consequences on research strategies for theoretical and applied biology.

GOVERNMENT DEBT AS THE INTEGRAL PORTFOLIO OF ASSETS AND LIABILITIES GENERATED BY DEBT

The paper analyses the possibilities of optimal government (national) debt management, trying to maximize the made-up net value for the debtor with the help of funds borrowed by the government. The integral portfolio of debtor assets and debt service liabilities, based on the borrowed funds, is chosen as a solution for the above-described problem. In the paper, an asset is understood as a position of government expenditures, where funds borrowed by the government are used and create a quantifiable profit (value) or the measurable damage or loss is avoided if funds are borrowed. Actually, liabilities are the main debt service positions. Naturally, the value generated by assets, as well as funds spent to settle the liabilities, could be analytically adequately evaluated only in stochastic dimension. Consequently, multidimensional multicriteria stochastic optimization technique is used as a technical solution to the formulated problem. In analytical decisions, the budget funds borrowed by the government are treated as marginal funds. Taking into account a completely new decision technique that has been invoked for government debt management, the methods of decisions are described quite particularly.

An Efficient Bayesian Calibration Approach Using Dynamically Biorthogonal Field Equations

Present paper proposes new dynamic-biorthogonality based Bayesian formulation for calibration of computer simulators with parametric uncertainty. The formulation uses decomposition of solution field into mean and random field. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spacial dimensions. Both the dimensions are spectrally represented using respective orthogonal bases. In particular, present paper investigates polynomial chaos basis for stochastic dimension and eigenfunction basis for spacial dimension. Dynamic evolution equations are derived such that basis in stochastic dimension is retained while basis in spacial dimension is changed such that dynamic orthogonality is maintained. Resultant evolution equations are used to propagate prior uncertainty in input parameters to the solution output. Whenever new information is available through experimental observations or expert opinion, Bayes theorem is used to update the basis in stochastic dimension. Efficacy of the proposed methodology is demonstrated for calibration of 2D transient diffusion equation with uncertainty in source location. Computational efficiency of the method is demonstrated against Generalized Polynomial Chaos and Monte Carlo method.