Rank 2 proximal Cantor systems are residually scrambled

Downarowicz and Maass [7 T. Downarowicz and A. Maass, Finite-rank Bratteli–Vershik diagrams are expansive, Ergod. Th. Dynam. Sys. 28 (2008), pp. 739–747.[Web of Science ®] , [Google Scholar]] proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this definition to the case of the essentially minimal zero-dimensional systems. We consider the cases in which topological ranks are 2 and unique minimal sets are fixed points. Akin and Kolyada [2 E. Akin and S. Kolyada, Li–Yorke sensitivity, Nonlinearity 16(4) (2003), pp. 1421–1433.[Crossref], [Web of Science ®] , [Google Scholar]], had shown that if the unique minimal set of an essentially minimal system is a fixed point, then the system must be proximal. The finite topological rank implies expansiveness; furthermore, in the case of proximal Cantor systems with topological rank 2, the expansiveness is always from the lowest degree. Rank 2 proximal Cantor systems are residually scrambled. We present a necessary and sufficient condition for the unique ergodicity of these systems. In addition, we show that the number of ergodic measures of the systems that are topologically mixing can be 1 and 2. Moreover, we present examples that are topologically weakly mixing, not topologically mixing, and uniquely ergodic. Finally, we show that the number of ergodic measures of the systems that are not weakly mixing can be 1 and 2.     

A Possible Magnetic Phase with Scalar Chirality in Solid 3He Layers

We study quantum effects in a system of S = 1/2 spins with two–, three and four–spin exchange interactions on the triangular lattice, a possible model of the nuclear magnetism of solid ³ He layers. The ground state phases found in our previous work are studied by using the linear spin–wave theory. The uuud state shows a very flat spin–wave dispersion, which suggests that this state, though locally stable, will not survive non–linear quantum effects. The tetrahedral state, which has long–range order of a scalar chirality, is found to be stable against spin wave fluctuations. The ground state energies of different phases are compared. Results of numerical analysis of finite size clusters are also presented.     

Anisotropy in the resistive superconducting transition under magnetic fields in single crystal Pb2Sr2Ho0.5Ca0.5Cu3O8

Anisotropie properties of the single crystal Pb₂Sr₂Ho_0.5Ca_0.5Cu₃O₈ have been investigated by measuring the electrical resistivity in theab-planeρ _ab (H, θ,T), which depends on the angleθ between theab-plane and the magnetic-field direction, in various constant fieldsH perpendicular to the current direction. All the angle-dependent values ofρ _ab (H, θ,T) at a constant temperature are scaled to be on one curve as a function of reduced field. The anisotropic parameter γ≡(m _c ^* /m _ab ^* )^1/2 is estimated as 12–13, which is larger than that of YBa₂Cu₃O₇ and much smaller than that of Bi₂Sr₂CaCu₂O₈. It has been concluded that the anisotropy does not always depend on the thickness of the blocking layer but seems to depend on the overlap of the electronic wave functions along thec-axis. Anisotropy in the pinning potential has also been discussed from the resistive tail in the temperature dependence ofρ _ab (H,θ,T).     

Curvature continuous path generation for autonomous vehicle using B-spline curves

In this paper we introduce a roadmap algorithm for generating collision-free paths in terms of cubic B-spline curves for unmanned vehicles used in mining operations. The algorithm automatically generates collision-free paths that are curvature continuous with an upper bounded curvature and a small slope discontinuity of curvature at knots, when we are given the locations of the obstacles, the boundary geometry of the working area, positions and directions of the vehicle at the start, loading, and the goal points. Our algorithm also allows us to find a switch back point where the vehicle reverses its direction to enter the loading area. Examples are provided to demonstrate the effectiveness of the proposed algorithms.     

Automatic detection of the topographical distribution of EEG rhythms based on an iterative adjustment of the averaged reference potential

Electroencephalogram (EEG) interpretation is important for the investigation of brain diseases. In this study, an automatic technique was developed to detect the topographical distribution of EEG rhythms. In order to obtain the topographical distribution, the amplitude of the EEG rhythm was analyzed based on the referential derivation where the reference potential was adjusted iteratively. The result of the automatic detection of the topographical distribution was helpful in highlighting the EEG rhythms of interest for automatic EEG interpretation. The technique developed has application significance for real clinics.     

Digital RAC with a disturbance observer for underwater vehicle-manipulator systems

Most control methods of underwater vehiclemanipulator systems (UVMS) are based on the computed torque method that is used for underwater robotic vehicles. We have proposed a resolved acceleration control (RAC) method for UVMS. In this article, we propose a disturbance compensation control method for both vehicle and manipulator based on the RAC method. Experimental results using an underwater robot with a vertical planar 2-link manipulator show that the proposed control method has good control performance.     

ProcDef: Local‐to‐global Deformation for Skeleton‐free Character Animation

Animations of characters with flexible bodies such as jellyfish, snails, and, hearts are difficult to design using traditional skeleton‐based approaches. A standard approach is keyframing, but adjusting the shape of the flexible body for each key frame is tedious. In addition, the character cannot dynamically adjust its motion to respond to the environment or user input. This paper introduces a new procedural deformation framework (ProcDef) for designing and driving animations of such flexible objects. Our approach is to synthesize global motions procedurally by integrating local deformations. ProcDef provides an efficient design scheme for local deformation patterns; the user can control the orientation and magnitude of local deformations as well as the propagation of deformation signals by specifying line charts and volumetric fields. We also present a fast and robust deformation algorithm based on shape‐matching dynamics and show some example animations to illustrate the feasibility of our framework.     

Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216–228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.     

Solving the irregular strip packing problem via guided local search for overlap minimization

The irregular strip-packing problem (ISP) requires a given set of non-convex polygons to be placed without overlap within a rectangular container having a fixed width and a variable length, which is to be minimized. As a core sub-problem to solve ISP, we consider an overlap minimization problem (OMP) whose objective is to place all polygons into a container with given width and length so that the total amount of overlap between polygons is made as small as possible. We propose to use directional penetration depths to measure the amount of overlap between a pair of polygons, and present an efficient algorithm to find a position with the minimum overlap for each polygon when it is translated in a specified direction. Based on this, we develop a local search algorithm for OMP that translates a polygon in horizontal and vertical directions alternately. Then we incorporate it in our algorithm for OMP, which is a variant of the guided local search algorithm. Computational results show that our algorithm improves the best-known values of some well-known benchmark instances.