A Molecular Implementation of the Least Mean Squares Estimator

In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide a powerful means to accomplish that goal. In this paper we show how the traditional LMS algorithm can be implemented at the molecular level using only a few elementary biomolecular reactions. We demonstrate our approach using several simulation studies and discuss its relevance to synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator, adaptive system

Path mutual information for a class of biochemical reaction networks

Living cells encode and transmit information in the temporal dynamics of biochemical components. Gaining a detailed understanding of the input-output relationship in biological systems therefore requires quantitative measures that capture the interdependence between complete time trajectories of biochemical components. Mutual information provides such a measure but its calculation in the context of stochastic reaction networks is associated with mathematical challenges. Here we show how to estimate the mutual information between complete paths of two molecular species that interact with each other through biochemical reactions. We demonstrate our approach using three simple case studies.Comment: 6 pages, 2 figure

Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach. For instance, we exemplarily formulate and solve a marginal master equation describing the protein translation and degradation in a fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio

Granularity of corporate debt : [Version 9 Mai 2013]

We study to what extent firms spread out their debt maturity dates across time, which we call "granularity of corporate debt." We consider the role of debt granularity using a simple model in which a firm's inability to roll over expiring debt causes inefficiencies, such as costly asset sales or underinvestment. Since multiple small asset sales are less costly than a single large one, firms may diversify debt rollovers across maturity dates. We construct granularity measures using data on corporate bond issuers for the 1991-2011 period and establish a number of novel findings. First, there is substantial variation in granularity in that many firms have either very concentrated or highly dispersed maturity structures. Second, our model's predictions are consistent with observed variation in granularity. Corporate debt maturities are more dispersed for larger and more mature firms, for firms with better investment opportunities, with higher leverage ratios, and with lower levels of current cash flows. We also show that during the recent financial crisis especially firms with valuable investment opportunities implemented more dispersed maturity structures. Finally, granularity plays an important role for bond issuances, because we document that newly issued corporate bond maturities complement pre-existing bond maturity profiles

A simple approach to the numerical simulation with trimmed CAD surfaces

In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM) or Boundary Element (BEM) software. The method is first verified with classical test examples in structural mechanics. Then two practical applications are presented one using the FEM, the other the BEM, that show the applicability of the method.Comment: 20 pages and 16 figure

Market implied costs of bankruptcy

This paper takes a novel approach to estimating bankruptcy costs by inference from market prices of equity and put options using a dynamic structural model of capital structure. This approach avoids the selection bias of looking at firms in or near default and therefore permits theories of ex ante capital structure determination to be tested. We identify significant cross sectional variation in bankruptcy costs across industries and relate these to specific firm characteristics. We find that asset volatility and growth options have significant positive impacts, while tangibility and size have negative impacts. Our bankruptcy cost variable estimate significantly negatively impacts leverage ratios. This negative impact is in addition to that of other firm characteristics such as asset intangibility and asset volatility. The results provide strong support for the tradeoff theory of capital structure

Sovereign bond risk premiums

Credit risk has become an important factor driving government bond returns. We therefore introduce an asset pricing model which exploits information contained in both forward interest rates and forward CDS spreads. Our empirical analysis covers euro-zone countries with German government bonds as credit risk-free assets. We construct a market factor from the first three principal components of the German forward curve as well as a common and a country-specific credit factor from the principal components of the forward CDS curves. We find that predictability of risk premiums of sovereign euro-zone bonds improves substantially if the market factor is augmented by a common and an orthogonal country-specific credit factor. While the common credit factor is significant for most countries in the sample, the country-specific factor is significant mainly for peripheral euro-zone countries. Finally, we find that during the current crisis period, market and credit risk premiums of government bonds are negative over long subintervals, a finding that we attribute to the presence of financial repression in euro-zone countries

Simulation of rock salt dissolution and its impact on land subsidence

Extensive land subsidence can occur due to subsurface dissolution of evaporites such as halite and gypsum. This paper explores techniques to simulate the salt dissolution forming an intrastratal karst, which is embedded in a sequence of carbonates, marls, anhydrite and gypsum. A numerical model is developed to simulate laminar flow in a subhorizontal void, which corresponds to an opening intrastratal karst. The numerical model is based on the laminar steady-state Stokes flow equation, and the advection dispersion transport equation coupled with the dissolution equation. The flow equation is solved using the nonconforming Crouzeix-Raviart (CR) finite element approximation for the Stokes equation. For the transport equation, a combination between discontinuous Galerkin method and multipoint flux approximation method is proposed. The numerical effect of the dissolution is considered by using a dynamic mesh variation that increases the size of the mesh based on the amount of dissolved salt. The numerical method is applied to a 2D geological cross section representing a Horst and Graben structure in the Tabular Jura of northwestern Switzerland. The model simulates salt dissolution within the geological section and predicts the amount of vertical dissolution as an indicator of potential subsidence that could occur. Simulation results showed that the highest dissolution amount is observed near the normal fault zones, and, therefore, the highest subsidence rates are expected above normal fault zones