Toward bio-inspired information processing with networks of nano-scale switching elements

Unconventional computing explores multi-scale platforms connecting molecular-scale devices into networks for the development of scalable neuromorphic architectures, often based on new materials and components with new functionalities. We review some work investigating the functionalities of locally connected networks of different types of switching elements as computational substrates. In particular, we discuss reservoir computing with networks of nonlinear nanoscale components. In usual neuromorphic paradigms, the network synaptic weights are adjusted as a result of a training/learning process. In reservoir computing, the non-linear network acts as a dynamical system mixing and spreading the input signals over a large state space, and only a readout layer is trained. We illustrate the most important concepts with a few examples, featuring memristor networks with time-dependent and history dependent resistances

Language-based Abstractions for Dynamical Systems

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366

On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results

AND-NOT logic framework for steady state analysis of Boolean network models

Finite dynamical systems (e.g. Boolean networks and logical models) have been used in modeling biological systems to focus attention on the qualitative features of the system, such as the wiring diagram. Since the analysis of such systems is hard, it is necessary to focus on subclasses that have the properties of being general enough for modeling and simple enough for theoretical analysis. In this paper we propose the class of AND-NOT networks for modeling biological systems and show that it provides several advantages. Some of the advantages include: Any finite dynamical system can be written as an AND-NOT network with similar dynamical properties. There is a one-to-one correspondence between AND-NOT networks, their wiring diagrams, and their dynamics. Results about AND-NOT networks can be stated at the wiring diagram level without losing any information. Results about AND-NOT networks are applicable to any Boolean network. We apply our results to a Boolean model of Th-cell differentiation

A Model of the Cellular Iron Homeostasis Network Using Semi-Formal Methods for Parameter Space Exploration

This paper presents a novel framework for the modeling of biological networks. It makes use of recent tools analyzing the robust satisfaction of properties of (hybrid) dynamical systems. The main challenge of this approach as applied to biological systems is to get access to the relevant parameter sets despite gaps in the available knowledge. An initial estimate of useful parameters was sought by formalizing the known behavior of the biological network in the STL logic using the tool Breach. Then, once a set of parameter values consistent with known biological properties was found, we tried to locally expand it into the largest possible valid region. We applied this methodology in an effort to model and better understand the complex network regulating iron homeostasis in mammalian cells. This system plays an important role in many biological functions, including erythropoiesis, resistance against infections, and proliferation of cancer cells.Comment: In Proceedings HSB 2012, arXiv:1208.315

Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)

In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study.Comment: In Proceedings CompMod 2011, arXiv:1109.104