Abstract-The symbolic time series generated by a unimodal chaotic map starting from any initial condition creates a binary sequence that contains information about the initial condition. A binary sequence of a given length generated this way has a one-toone correspondence with a given range of the input signal. This can be used to construct analogue to digital converters (ADC). However, in actual circuit realizations, component imperfections and ambient noise result in deviations in the map function from the ideal, which, in turn, can cause significant error in signal measurement. In this paper, we propose ways of circumventing these problems through an algorithmic procedure that takes into account the non-idealities. The most common form of nonideality-reduction in the height of the map function-alters the partitions that correspond to each symbolic sequence. We show that it is possible to define the partitions correctly if the height of the map function is known. We also propose a method to estimate this height from the symbolic sequence obtained. We demonstrate the efficacy of the proposed algorithm with simulation as well as experiment. With this development, practical ADCs utilizing chaotic dynamics may become reality.

Many physical situations involve chaotic systems implemented in hardware. Among them onedimensional piecewise linear maps are popular candidates for such applications because of their property of generating robust chaos. In physical implementations, the control parameter of these maps may deviate from its ideal value due to hardware imprecision. Since the dynamics of a chaotic map is completely defined by its control parameter, one needs to know the value of the parameter in a hardware realisation. In this paper, we show that it is possible to determine the parameter, through the realisation of the unstable fixed point of the map, by utilising noise that is always present in the system. We present this in the form of an algorithm and demonstrate its efficacy through simulated results. We also determine the bounds on the signal-to-noise ratio required for successful parameter estimation. The proposed approach is expected to be beneficial to the existing noise reduction techniques and time series recovery algorithms that require a reasonably accurate knowledge of the map.

<p>Seasonal evolution of Arctic sea ice floe is caused by various fragmentation and melt processes. Those include melt fragmentation in summer due to weaker part of floe by melt ponds, legacy re-frozen leads or cracks, as well as mechanical breakup in spring due to ice deformation forcing. Understanding these fragmentation processes is important not only to evaluate recent Arctic sea ice decline, but also to improve climate models for the Arctic. The objective of this study is to investigate those fragmentation processes at individual floe scales, with hypothesis that fractal properties may differ between melt fragmentation and mechanical breakup. With that in mind, we collected the “floe-scale” data set of 1-m MEDEA images that contain floe-scale imagery before and after fragmentation, and calculated the floe size, perimeter and fractal properties at the floe scale. In this presentation, we will share preliminary results of those analysis, including the role of melt ponds and legacy refrozen leads or cracks in melt fragmentation and difference in fractal properties between melt fragmentation and mechanical breakup.</p>