Symmetry in Critical Random Boolean Network Dynamics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems

Phase Diagram for a 2-D Two-Temperature Diffusive XY Model

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.Comment: 5 pages, 4 figure

Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes

Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior of a node regardless of the remaining input. It has been shown that Boolean networks can become canalized if they evolve through a frustrated competition between nodes. This was demonstrated for large networks in which each node had K=3 inputs. Those networks evolve to a critical steady-state at the boarder of two phases of dynamical behavior. Moreover, the evolution of these networks was shown to be associated with the symmetry of the evolutionary dynamics. We extend these results to the more highly connected K>3 cases and show that similar canalized critical steady states emerge with the same associated dynamical symmetry, but only if the evolutionary dynamics is biased toward homogeneous Boolean functions.Comment: 8 pages, 5 figure

Do You Need a Foot-in-the-Door or Is A Toe Enough? Scripting Introductions That Induce Tailoring and Increase Participation in Telephone Interviews

Substantial research and practical experience shows that a telephone interviewer is most successful at gaining cooperation and avoiding refusals when they are free to tailor their introductory pitch to the potential respondent or household informant they reach. However, survey designers are often uncomfortable allowing interviewers to work “off-script,” and instruct interviewers to read introductory text verbatim. Further, some interviewers report being more comfortable with a script than without one. To bridge this gap between research and practice we asked, “Can we create a scripted introduction that engages the potential respondent, gets a foot-in-the-door, and facilitates interviewer tailoring?” This paper reports on a randomized experimental test of two such scripts, each implemented within the Washington Behavioral Risk Factor Surveillance System (BRFSS), a random digit dial (RDD) phone survey. In both phases of the experiment, sampled phone numbers were randomized to the standard BRFSS introduction or the new script. Phase 1 (August, 2018) implemented a “conversational” introduction that added or revised three features of the standard BRFSS introduction: First, the introduction included three “hook questions” (e.g., “Have you heard of the survey?”). One hook question was randomly displayed each time a phone number was called. Second, the script displayed on the first three CATI screens was modified to sound more conversational and less abrupt. Third, pause points were created to make sure the interviewer slows down and listens to the potential respondent. Each of these features is hypothesized to increase tailoring, and thus cooperation, by encouraging interaction between the interviewer and potential respondent. Phase 2 (September, 2018) replaced the conversational introduction with a “progressive scheduling” script that instructed interviewers to ask for a good time to call back to complete the interview rather than asking for complete cooperation on the call. This approach encourages a dynamic that shows respect for the respondent’s time. It also changes a large, unexpected request to a small one that the respondent can plan. While call-backs are sometimes considered undesirable outcomes, they can be a good “toe-in-the-door” technique that leads to full cooperation later. Our primary outcomes are cooperation, scheduled callbacks, and refusals. Additionally, a more conversational introduction might influence answers to questions within the interview, such as if increased rapport depresses reports of sensitive behaviors. Thus, we will also assess the effect of the modified scripts on responses to assess the nonresponse / measurement error trade-offs of this approach