A Generalization of the Fujisawa–Kuh Global Inversion Theorem

We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity

Protein synthesis driven by dynamical stochastic transcription

In this manuscript we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.Comment: 20 pages, 3 figure

ODEbase: A Repository of ODE Systems for Systems Biology

Recently, symbolic computation and computer algebra systems have beensuccessfully applied in systems biology, especially in chemical reactionnetwork theory. One advantage of symbolic computation is its potential forqualitative answers to biological questions. Qualitative methods analyzedynamical input systems as formal objects, in contrast to investigating onlypart of the state space, as is the case with numerical simulation. However,symbolic computation tools and libraries have a different set of requirementsfor their input data than their numerical counterparts. A common format used inmathematical modeling of biological processes is SBML. We illustrate that theuse of SBML data in symbolic computation requires significant pre-processing,incorporating external biological and mathematical expertise. ODEbase provideshigh quality symbolic computation input data derived from established existingbiomodels, covering in particular the BioModels database.<br

Time-lapse electrical resistivity anomalies due to contaminant transport around landfills

The extent of landfill leachate can be delineated by geo-electrical imaging as a response to the varying electrical resistivity in the contaminated area. This research was based on a combination of hydrogeological numerical simulation followed by geophysical forward and inversion modeling performed to evaluate the migration of a contaminant plume from a landfill. As a first step, groundwater flow and contaminant transport was simulated using the finite elements numerical modeling software FEFLOW. The extent of the contaminant plume was acquired through a hydrogeological model depicting the distributions of leachate concentration in the system. Next, based on the empirical relationship between the concentration and electrical conductivity of the leachate in the porous media, the corresponding geo-electrical structure was derived from the hydrogeological model. Finally, forward and inversion computations of geo-electrical anomalies were performed using the finite difference numerical modeling software DCIP2D/DCIP3D. The image obtained by geophysical inversion of the electric data was expected to be consistent with the initial hydrogeological model, as described by the distribution of leachate concentration. Numerical case studies were conducted for various geological conditions, hydraulic parameters and electrode arrays, from which conclusions were drawn regarding the suitability of the methodology to assess simple to more complex geo-electrical models. Thus, optimal mapping and monitoring configurations were determined

When IoT Meets DevOps: Fostering Business Opportunities

The Internet of Things (IoT) is the new digital revolution for the near-future society, the second after the creation of the Internet itself. The software industry is converging towards the large-scale deployment of IoT devices and services, and there’s broad support from the business environment for this engineering vision. The Development and Operations (DevOps) project management methodology, with continuous delivery and integration, is the preferred approach for achieving and deploying applications to all levels of the IoT architecture. In this paper we also discuss the promising trend of associating devices with microservices, which are further encapsulated into functional packages called containers. Docker is considered the market leader in container-based service delivery, though other important software companies are promoting this concept as part of the technology solution for their IoT customers. In the experimental section we propose a three-layer IoT model, business-oriented, and distributed over multiple cloud environments, comprising the Physical, Fog/Edge, and Application layers. &nbsp; &nbsp; Keywords: Internet-of-Things, software technologies, project management, business environment Heading

Algorithmic Reduction of Biological Networks With Multiple Time Scales

We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting using a recent result by Cardin and Teixeira. The existence of invariant manifolds is subject to hyperbolicity conditions, which we test algorithmically using Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations