Efficient Bayesian Learning in Social Networks with Gaussian Estimators

We consider a group of Bayesian agents who try to estimate a state of the world $\theta$ through interaction on a social network. Each agent $v$ initially receives a private measurement of $\theta$: a number $S_v$ picked from a Gaussian distribution with mean $\theta$ and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of $\theta$ to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have, had they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most $2N \cdot D$ steps, where $N$ is the number of agents and $D$ is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after $D$ steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.Comment: Added coauthor. Added proofs for fast convergence on trees and distance transitive graphs. Also, now analyzing a notion of privac

Influence of a cavity on the dynamical behaviour of an airfoil

A new wing design has been the subject of study in the European project VortexCell2050. For several reasons (structural and fuel load) it is desirable to use relatively thick wings. However, thick wings promote flow separation and/or massive vortex shedding, reducing flight performance. The new design airfoil is equipped with a cavity ("vortex cell") in the wing in order to prevent massive flow separation. This thesis aims to obtain insight into the dynamical behaviour of such a wing with a cavity and to explore which numerical methods are suitable for estimating the unsteady forces. In this thesis experiments and computations are presented, using a geometry that was inspired by cavity shapes which are considered in the VortexCell2050 project. For an airfoil with a cavity, oscillations of the shear layer are expected at Strouhal numbers of order unity, based on the width of the cavity opening. For the size of the cavities considered this implies high values, O(10), of the reduced frequency, based on the chord length of the airfoil. In order to conduct experiments in this high reduced frequency range, a new experimental method has been developed. In this experimental setup the airfoil is fixed to the wind tunnel wall and the first acoustic transversal eigenmode of the wind tunnel test section is used to drive an oscillating flow. In the conventional method the airfoil is oscillating. The main fundamental difference between the two methods is the presence of a time dependent uniform pressure gradient, which drives the oscillating flow, in the new method. The results obtained with both methods are equivalent after correcting for an effective buoyancy force induced by this driving pressure gradient. The new method avoids the use of a complex mechanical system to drive the oscillation of the airfoil. The acoustical forcing amplitude is very easy to vary within two orders of magnitude. The method appears to be most suitable for the conduction of experiments at high values of the reduced frequency. The new measurement method is validated by means of experiments on a standard NACA0018 airfoil complemented with two-dimensional Euler simulations. Thereafter two airfoils with slightly different cavity geometries are investigated in the wind tunnel. These experiments consist of measurements of local surface pressures. For the case of an airfoil with a cavity the Euler equations are not suitable. Two-dimensional simulations using the frictionlass flow approximation approach a so-called Batchelor flow, with a uniform rotation in the cavity. This flow is not observed in experiments. For this reason two-dimensional incompressible Navier–Stokes simulations at a Reynolds number, based on the chord length of the airfoil, of 2 · 104 are performed and indicate shear layer oscillations. In order to validate these low Reynolds number numerical results and to gain more insight in the flow physics, flow visualisations are performed in a waterchannel at the same Reynolds numbers as the numerical simulations. The visualisations also show oscillations of the shear layer at the first and second hydrodynamic mode, this is confirmed by hot-wire measurements in the wind tunnel at low Reynolds numbers. The hot-wire measurements also demonstrate that the expected lock-in of the shear layer does occur in a limited range of Reynolds numbers, based on the chord, sufficiently low such that no turbulence is generated, but higher than a critical value. Experiments and two-dimensional Navier–Stokes simulations indicate that for values of the reduced frequency, in the range of 2–10, no significant deviations in the unsteady lift force occur between an airfoil with cavity and the same airfoil without cavity. The cavity does display shear layer oscillations around the expected Strouhal numbers, however, the associated fluctuations in the lift coefficient appear to be neglegible. For the geometries considered the pressure differences over the airfoil are dominated by the added mass of the airfoil

Allosteric proteins as logarithmic sensors

Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes

Numerical Simulation of Flow over an Airfoil with a Cavity

Two-dimensional direct numerical simulation of the flow over a NACA0018 airfoil with a cavity is presented. The low Reynolds number simulations are validated by means of flow visualizations carried out in a water channel. From the simulations, it follows that there are two main regimes of flow inside the cavity. Depending on the angle of attack, the first or the second shear-layer mode (Rossiter tone) is present. The global effect of the cavity on the flow around the airfoil is the generation of vortices that reduce flow separation downstream of the cavity. At high positive angles of attack, the flow separates in front of the cavity, and the separated flow interacts with the cavity, causing the generation of smaller-scale structures and a narrower wake compared with the case when no cavity is present. At certain angles of attack, the numerical results suggest the possibility of a higher lift-to-drag ratio for the airfoil with cavity compared with the airfoil without cavity

Designing for Collaboration Using Social Network Analysis: Towards a Conceptual Method to Understand Organisational Interaction

The spreading of innovation within organisations is an area of interest for both academics and practitioners. Within information systems research collaboration issues are often addressed and solved through implementation of technology artefacts to meditate communication. With more and more resources being spent on collaborative technologies we argue that there can be cost advantages in looking at the socio-technical aspects of the information system when trying improve organisational communication. As an initial step of information system interventions we argue that an overview of the information exchange network within organisations can lead to valuable insights into where to start and we argue that social network analysis can provide such an bird’s-eye view over organisational interaction. This leads us to our research question: How can social network analysis be used to describe, understand and explain organisational interaction in designing information systems for collaboration? Taking a design science approach to the research question we aim to construct a meta-artefact, i.e. in our case knowledge about how to design for collaboration with the help of social network analysis. To test the applicability of social network analysis we collect sociometric interaction data from a knowledge intensive organisation using a name generating survey. The usability of the visualisations that are the output of the social network analysis are evaluated by decision makers within the organisation through interviews. We conclude that social network analysis is a time-efficient method of collecting empirical data that can lead to deep insights into the structure of the organisational communication network. The visualisation can be seen as a map used to pinpoint the emergence of social networks within organisations and thereby acting as a tool to drive continuous change and innovation

Architecture, Design, and Tradeoffs in Biomolecular Feedback Systems

A core pursuit in systems and synthetic biology is the analysis of the connection between the low-level structure and parameters of a biomolecular network and its high-level function and performance. Elucidating this mapping has become increasingly feasible as precise measurements of both input parameters and output dynamics become abundant. At the same time, cross-pollination between biology and engineering has led to the realization that many of the mathematical tools from control theory are well-suited to analyze biological processes. The goal of this thesis is to use tools from control theory to analyze a variety of biomolecular systems from both natural and synthetic settings, and subsequently yield insight into the architecture, tradeoffs, and limitations of biological network. In Chapter 2, I demonstrate how allosteric proteins can be used to respond logarithmically to changes in signal. In Chapter 3, I show how control theoretic techniques can be used to inform the design of synthetic integral feedback networks that implement feedback with a sequestration mechanism. Finally, in Chapter 4 I present a novel simplified model of the E. coli heat shock response system and show how the the mapping of circuit parameters to function depends on the network's architecture. The unifying theme of this research is that the conceptual framework used to study engineered systems is remarkably well-suited to biology. That being said, it is important to apply these tools in a way that is informed by the molecular details of biological processes. By combining structural and biochemical data with the functional perspective of engineering, it is possible to understand the architectural principles that underlie living systems.</p

Design Guidelines For Sequestration Feedback Networks

Integral control is commonly used in mechanical and electrical systems to ensure perfect adaptation. A proposed design of integral control for synthetic biological systems employs the sequestration of two biochemical controller species. The unbound amount of controller species captures the integral of the error between the current and the desired state of the system. However, implementing integral control inside bacterial cells using sequestration feedback has been challenging due to the controller molecules being degraded and diluted. Furthermore, integral control can only be achieved under stability conditions that not all sequestration feedback networks fulfill. In this work, we give guidelines for ensuring stability and good performance (small steady-state error) in sequestration feedback networks. Our guidelines provide simple tuning options to obtain a flexible and practical biological implementation of sequestration feedback control. Using tools and metrics from control theory, we pave the path for the systematic design of synthetic biological systems