Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences

In this paper, we propose to mix the approach underlying Bandt-Pompe permutation entropy with Lempel-Ziv complexity, to design what we call Lempel-Ziv permutation complexity. The principle consists of two steps: (i) transformation of a continuous-state series that is intrinsically multivariate or arises from embedding into a sequence of permutation vectors, where the components are the positions of the components of the initial vector when re-arranged; (ii) performing the Lempel-Ziv complexity for this series of `symbols', as part of a discrete finite-size alphabet. On the one hand, the permutation entropy of Bandt-Pompe aims at the study of the entropy of such a sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state sequence aims at the study of the temporal organization of the symbols (i.e., the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation complexity aims to take advantage of both of these methods. The potential from such a combined approach - of a permutation procedure and a complexity analysis - is evaluated through the illustration of some simulated data and some real data. In both cases, we compare the individual approaches and the combined approach.Comment: 30 pages, 4 figure

Experimental realization of a Dirac monopole through the decay of an isolated monopole

We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually evolves into a spin configuration hosting a Dirac monopole in its synthetic magnetic field. We characterize in detail the Dirac monopole by measuring the particle densities of the spin states projected along different quantization axes. Importantly, we observe the spontaneous emergence of nodal lines in the condensate density that accompany the Dirac monopole. We also demonstrate that the monopole decay accelerates in weaker magnetic field gradients.Comment: 10 pages, 7 figure

Transcoding of MPEG Bitstreams

This paper discusses the problem of transcoding as it may occur in, for instance, the following situation. Suppose a satellite transmits an MPEG-compressed video signal at say 9 Mbit/s. This signal must be relayed at a cable head end. However, since the cable capacity is only limited, the cable head end will want to relay this incoming signal at a lower bit-rate of, say, 5 Mbit/s. The problem is how to convert a compressed video signal of a given bit-rate into a compressed video signal of a lower bit-rate. The specific transcoding problem discussed in this paper is referred to as bit-rate conversion. Basically, a transcoder used for such a purpose will consist of a cascaded decoder and encoder. It is shown in the paper that the complexity of this combination can be significantly reduced. The paper also investigates the loss of picture quality that may be expected when a transcoder is in the transmission chain. The loss of quality as compared to that resulting in the case of transmission without a transcoder is studied by means of computations using simplified models of the transmission chains and by means of using computer simulations of the complete transmission chain. It will be shown that the presence of two quantizers, i.e. cascaded quantization, in the transmission chain is the main cause of extra losses, and it will be shown that the losses in terms of SNR will be some 0.5 ¿ 1.0 dB greater than in the case of a transmission chain without a transcoder

Explicit model predictive control accuracy analysis

Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line partition of the state space into non-overlapped convex regions, with affine control laws associated to each region of the partition. An actual implementation of this explicit MPC in low cost micro-controllers requires the data to be "quantized", i.e. represented with a small number of memory bits. An aggressive quantization decreases the number of bits and the controller manufacturing costs, and may increase the speed of the controller, but reduces accuracy of the control input computation. We derive upper bounds for the absolute error in the control depending on the number of quantization bits and system parameters. The bounds can be used to determine how many quantization bits are needed in order to guarantee a specific level of accuracy in the control input.Comment: 6 pages, 7 figures. Accepted to IEEE CDC 201

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold a great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits robust resonant Andreev reflection and 2e2/h quantized conductance at low temperature. By utilizing variable-tunnel-coupled scanning tunneling spectroscopy, we study tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance. In contrast, no such plateau behaviors were observed on either finite energy Caroli-de Genne-Matricon bound states or in the continuum of electronic states outside the superconducting gap. This unique behavior of the zero-mode conductance reaching a plateau strongly supports the existence of MZMs in this iron-based superconductor, which serves as a promising single-material platform for Majorana braiding at a relatively high temperature