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Register a new userInter-Scale Information Flow as a Surrogate for Downward Causation That Maintains Spiral Waves
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The mechanism that maintains atrial fibrillation (AF) remains elusive. One approach to understanding and controlling the mechanism (AF driver) is to quantify inter-scale information flow from macroscopic to microscopic behaviors of the cardiac system as a surrogate for the downward causation of the AF driver. We use a numerical model of a cardiac system with one of the potential AF drivers, a rotor, the rotation center of spiral waves, and generate a renormalization group with system descriptions at multiple scales. We find that transfer entropy accurately quantifies the upward and downward information flow between microscopic and macroscopic descriptions of the cardiac system with spiral waves. Because the spatial profile of transfer entropy and intrinsic transfer entropy is identical, there are no synergistic effects in the system. We also find that inter-scale information flow significantly decreases as the description of the system becomes more macroscopic. The downward information flow is significantly smaller than the upward information flow. Lastly, we find that downward information flow from macroscopic to microscopic descriptions of the cardiac system is significantly correlated with the number of rotors, but the higher number of rotors is not necessarily associated with a higher downward information flow. This result contradicts the concept that the rotors are the AF driver, and may account for the conflicting evidence from clinical studies targeting rotors as the AF driver.
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Spiral waves are considered to be one of the potential mechanisms that maintains complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of finite-time Lyapunov exponent (FTLE) between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes from along the line of centres to perpendicular to the line of centres as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wavenumber and frequency are determined. These depend on the positions of the centres of the spirals, and so evolve slowly as the spirals move.
We study the dynamics of a ferrofluid thin film confined in a Hele-Shaw cell, and subjected to a tilted nonuniform magnetic field. It is shown that the interface between the ferrofluid and an inviscid outer fluid (air) supports traveling waves, governed by a novel modified Kuramoto--Sivashinsky-type equation derived under the long-wave approximation. The balance between energy production and dissipation in this long-wave equations allows for the existence of dissipative solitons. These permanent traveling waves propagation velocity and profile shape are shown to be tunable via the external magnetic field. A multiple-scale analysis is performed to obtain the correction to the linear prediction of the propagation velocity, and to reveal how the nonlinearity arrests the linear instability. The traveling periodic interfacial waves discovered are identified as fixed points in an energy phase plane. It is shown that transitions between states (wave profiles) occur. These transitions are explained via the spectral stability of the traveling waves. Interestingly, multiperiodic waves, which are a non-integrable analog of the double cnoidal wave, also found to propagate under the model long-wave equation. These multiperiodic solutions are investigated numerically, and they are found to be long-lived transients, but ultimately abruptly transition to one of the stable periodic states identified above.
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schrodinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson, and Zakharov models. The solutions that we find are ones previously identified through different methods. Nevertheless, they highlight an important aspect of these structures, namely their self-similarity. They thus offer an alternative tool in the very sparse (outside of the inverse scattering method) toolbox of attempting to identify analytically (or computationally) rogue wave solutions. This methodology is importantly independent of the notion of integrability. An additional nontrivial motivation for such a formulation is that it offers a frame in which the rogue waves are stationary. It is conceivable that in this frame one could perform a proper stability analysis of the structures.
It is common to prove by reasoning over source code that programs do not leak sensitive data. But doing so leaves a gap between reasoning and reality that can only be filled by accounting for the behaviour of the compiler. This task is complicated when programs enforce value-dependent information-flow security properties (in which classification of locations can vary depending on values in other locations) and complicated further when programs exploit shared-variable concurrency. Prior work has formally defined a notion of concurrency-aware refinement for preserving value-dependent security properties. However, that notion is considerably more complex than standard refinement definitions typically applied in the verification of semantics preservation by compilers. To date it remains unclear whether it can be applied to a realistic compiler, because there exist no general decomposition principles for separating it into smaller, more familiar, proof obligations. In this work, we provide such a decomposition principle, which we show can almost halve the complexity of proving secure refinement. Further, we demonstrate its applicability to secure compilation, by proving in Isabelle/HOL the preservation of value-dependent security by a proof-of-concept compiler from an imperative While language to a generic RISC-style assembly language, for programs with shared-memory concurrency mediated by locking primitives. Finally, we execute our compiler in Isabelle on a While language model of the Cross Domain Desktop Compositor, demonstrating to our knowledge the first use of a compiler verification result to carry an information-flow security property down to the assembly-level model of a non-trivial concurrent program.
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