Theory of Interface: Category Theory, Directed Networks and Evolution of Biological Networks

Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this paper, first we discuss that these two modes can be associated with the category theoretic duality (adjunction) and derive a natural network structure (a path notion) for each mode by appealing to the category theoretic universality. The path notion corresponding to the static mode is just the usual directed path. The path notion for the dynamic mode is called lateral path which is the alternating path considered on the set of arcs. Their general functionalities in a network are transport and coherence, respectively. Second, we introduce a betweenness centrality of arcs for each mode and see how the two modes are embedded in various real biological network data. We find that there is a trade-off relationship between the two centralities: if the value of one is large then the value of the other is small. This can be seen as a kind of division of labor in a network into transport on the network and coherence of the network. Finally, we propose an optimization model of networks based on a quality function involving intensities of the two modes in order to see how networks with the above trade-off relationship can emerge through evolution. We show that the trade-off relationship can be observed in the evolved networks only when the dynamic mode is dominant in the quality function by numerical simulations. We also show that the evolved networks have features qualitatively similar to real biological networks by standard complex network analysis.Comment: 59 pages, minor corrections from v

Mapping tori of small dilatation irreducible train-track maps

We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound $M$ depending only on P, so that there exists a presentation of the fundamental group of the mapping torus of a P--small irreducible train-track map with less than M generators and M relations.Comment: Some figures in colo

The composition of Event-B models

The transition from classical B [2] to the Event-B language and method [3] has seen the removal of some forms of model structuring and composition, with the intention of reinventing them in future. This work contributes to thatreinvention. Inspired by a proposed method for state-based decomposition and refinement [5] of an Event-B model, we propose a familiar parallel event composition (over disjoint state variable lists), and the less familiar event fusion (over intersecting state variable lists). A brief motivation is provided for these and other forms of composition of models, in terms of feature-based modelling. We show that model consistency is preserved under such compositions. More significantly we show that model composition preserves refinement

Modularity for Security-Sensitive Workflows

An established trend in software engineering insists on using components (sometimes also called services or packages) to encapsulate a set of related functionalities or data. By defining interfaces specifying what functionalities they provide or use, components can be combined with others to form more complex components. In this way, IT systems can be designed by mostly re-using existing components and developing new ones to provide new functionalities. In this paper, we introduce a notion of component and a combination mechanism for an important class of software artifacts, called security-sensitive workflows. These are business processes in which execution constraints on the tasks are complemented with authorization constraints (e.g., Separation of Duty) and authorization policies (constraining which users can execute which tasks). We show how well-known workflow execution patterns can be simulated by our combination mechanism and how authorization constraints can also be imposed across components. Then, we demonstrate the usefulness of our notion of component by showing (i) the scalability of a technique for the synthesis of run-time monitors for security-sensitive workflows and (ii) the design of a plug-in for the re-use of workflows and related run-time monitors inside an editor for security-sensitive workflows

Shapes of topological RNA structures

A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1304.739

PLTL Partitioned Model Checking for Reactive Systems under Fairness Assumptions

We are interested in verifying dynamic properties of finite state reactive systems under fairness assumptions by model checking. The systems we want to verify are specified through a top-down refinement process. In order to deal with the state explosion problem, we have proposed in previous works to partition the reachability graph, and to perform the verification on each part separately. Moreover, we have defined a class, called Bmod, of dynamic properties that are verifiable by parts, whatever the partition. We decide if a property P belongs to Bmod by looking at the form of the Buchi automaton that accepts the negation of P. However, when a property P belongs to Bmod, the property f => P, where f is a fairness assumption, does not necessarily belong to Bmod. In this paper, we propose to use the refinement process in order to build the parts on which the verification has to be performed. We then show that with such a partition, if a property P is verifiable by parts and if f is the expression of the fairness assumptions on a system, then the property f => P is still verifiable by parts. This approach is illustrated by its application to the chip card protocol T=1 using the B engineering design language

Quick-cast: A method for fast and precise scalable production of fluid-driven elastomeric soft actuators

Fluid-driven elastomeric actuators (FEAs) are among the most popular actuators in the emerging field of soft robotics. Intrinsically compliant, with continuum of motion, large strokes, little friction, and high power-to-weight ratio, they are very similar to biological muscles, and have enabled new applications in automation, architecture, medicine, and human-robot interaction. To foster future applications of FEAs, in this paper we present a new manufacturing method for fast and precise scalable production of complex FEAs of high quality (leak-free, single-body form, with <0.2 mm precision). The method is based on 3d moulding and supports elastomers with a wide range of viscosity, pot life, and Young's modulus. We developed this process for two different settings: one in laboratory conditions for fast prototyping with 3d printed moulds and using multi-component liquid elastomers, and the other process in an industrial setting with 3d moulds micromachined in metal and applying compression moulding. We demonstrate these methods in fabrication of up to several tens of two-axis, three-chambered soft actuators, with two types of chamber walls: cylindrical and corrugated. The actuators are then applied as motion drivers in kinetic photovoltaic building envelopes