Planar Formation Control of a School of Robotic Fish: Theory and Experiments

This paper presents a nonlinear control design for the stabilization of parallel and circular motion in a school of robotic fish actuated with internal reaction wheels. The closed-loop swimming dynamics of the fish robots are represented by the canonical Chaplygin sleigh. They exchange relative state information according to a connected, undirected communication graph to form a system of coupled, nonlinear, second-order oscillators. Prior work on collective motion of constant-speed, self-propelled particles serves as the foundation of our approach. However, unlike a self-propelled particle, the fish robots follow limit-cycle dynamics to sustain periodic flapping for forward motion with time-varying speed. Parallel and circular motions are achieved in an average sense without feedback linearization of the agents’ dynamics. Implementation of the proposed parallel formation control law on an actual school of soft robotic fish is described, including system identification experiments to identify motor dynamics and the design of a motor torque-tracking controller to follow the formation torque control. Experimental results demonstrate a school of four robotic fish achieving parallel formations starting from random initial conditions.

Power law behavior of Elementary Cellular Automata

This paper shows that the percolation clusters from elementary cellular automata {30, 45, 60, 86, 99, 105, 129, 150, 153, 169, 182, 183, 184, 195 and 225 exhibit strong power law behavior, either under random initial conditions, a single occupied cell, or both. Most of the tail exponents are less than unity, implying diverging means and variances of cluster sizes. The analysis presented here is admittedly coarse in an effort to expedite its dissemination.

Simulations of domain walls in Two Higgs Doublet Models

The Two Higgs Doublet Model predicts the emergence of 3 distinct domain wall solutions arising from the breaking of 3 accidental global symmetries, Z2, CP1 and CP2, at the electroweak scale for specific choices of the model parameters. We present numerical kink solutions to the field equations in all three cases along with dynamical simulations of the models in (2+1) and (3+1) dimensions. For each kink solution we define an associated topological current. In all three cases simulations produce a network of domain walls which deviates from power law scaling in Minkowski and FRW simulations. This deviation is attributed to a winding of the electroweak group parameters around the domain walls in our simulations. We observe a local violation of the neutral vacuum condition on the domain walls in our simulations. This violation is attributed to relative electroweak transformations across the domain walls which is a general feature emerging from random initial conditions.

Hybrid Chaotic Method for Medical Images Ciphering

Healthcare is an essential application of e-services, where for diagnostic testing, medical imaging acquiring, processing, analysis, storage, and protection are used. Image ciphering during storage and transmission over the networks used has seen implemented using many types of ciphering algorithms for security purpose. Current cyphering algorithms are classified into two types: traditional classical cryptography using standard algorithms (DES, AES, IDEA, RC5, RSA, ...) and chaos cryptography using continuous (Chau, Rossler, Lorenz, ...) or discreet (Logistics, Henon, ...) algorithms. The traditional algorithms have struggled to combat image data as compared to regular textual data. Whereas, the chaotic algorithms are more efficient for image ciphering. The Significancecharacteristics of chaos are its extreme sensitivity to initial conditions and algorithm parameters. In this paper, medical image security based on hybrid/mixed chaotic algorithms is proposed. The proposed method is implemented using MATLAB. Where the image of the Retina of the Eye to detect Blood Vessels is ciphered. The Pseudo-Random Numbers Generators (PRNGs) from the different chaotic algorithms are implemented, and their statistical properties are evaluated using the National Institute of Standards and Technology NIST and other statistical test-suits. Then, these algorithms are used to secure the data, where the statistical properties of the cipher-text are also tested. We propose two PRNGs to increase the complexity of the PRNGs and to allow many of the NIST statistical tests to be passed: one based on twohybrid mixed chaotic logistic maps and one based on two-hybrid mixed chaotic Henon maps, where each chaotic algorithm runs side-by-side andstarts with random initial conditions and parameters (encryption keys). The resulting hybrid PRNGs passed many of the NIST statistical test suits.

An Investigation into the Origin of Autopoiesis

Using a glider in the Game of Life cellular automaton as a toy model of minimal persistent individuals, this article explores how questions regarding the origin of life might be approached from the perspective of autopoiesis. Specifically, I examine how the density of gliders evolves over time from random initial conditions and then develop a statistical mechanics of gliders that explains this time evolution in terms of the processes of glider creation, persistence, and destruction that underlie it.

Spherically Restricted Random Hyperbolic Diffusion

This paper investigates solutions of hyperbolic diffusion equations in R 3 with random initial conditions. The solutions are given as spatial-temporal random fields. Their restrictions to the unit sphere S 2 are studied. All assumptions are formulated in terms of the angular power spectrum or the spectral measure of the random initial conditions. Approximations to the exact solutions are given. Upper bounds for the mean-square convergence rates of the approximation fields are obtained. The smoothness properties of the exact solution and its approximation are also investigated. It is demonstrated that the Hölder-type continuity of the solution depends on the decay of the angular power spectrum. Conditions on the spectral measure of initial conditions that guarantee short- or long-range dependence of the solutions are given. Numerical studies are presented to verify the theoretical findings.

Properties of $\varphi$-sub-Gaussian stochastic processes related to the heat equation with random initial conditions

In this paper, there are studied sample paths properties of stochastic processes representing solutions (in $L_2(\Omega)$ sense) of the heat equation with random initial conditions given by $\varphi$-sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded and unbounded domains.