Wandering intervals and absolutely continuous invariant probability measures of interval maps

For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove the nonexistence of wandering intervals, the existence of absolutely continuous invariant measures, and the bounded backward contraction property. The proofs are based on the method of proving the existence of absolutely continuous invariant measures of unimodal map, developed by Nowicki and van Strien.Comment: 16 pages, 2 figure

Wireless Communications in the Era of Big Data

The rapidly growing wave of wireless data service is pushing against the boundary of our communication network's processing power. The pervasive and exponentially increasing data traffic present imminent challenges to all the aspects of the wireless system design, such as spectrum efficiency, computing capabilities and fronthaul/backhaul link capacity. In this article, we discuss the challenges and opportunities in the design of scalable wireless systems to embrace such a "bigdata" era. On one hand, we review the state-of-the-art networking architectures and signal processing techniques adaptable for managing the bigdata traffic in wireless networks. On the other hand, instead of viewing mobile bigdata as a unwanted burden, we introduce methods to capitalize from the vast data traffic, for building a bigdata-aware wireless network with better wireless service quality and new mobile applications. We highlight several promising future research directions for wireless communications in the mobile bigdata era.Comment: This article is accepted and to appear in IEEE Communications Magazin

Mouse Tracking for Reading (MoTR): A New Incremental Processing Paradigm

This master’s thesis presents Mouse Tracking for Reading (MoTR), a new incre- mental processing measurement paradigm that can serve as an alternative to eye- tracking in places where no eye-tracking equipment is available. MoTR operates directly within a web browser, allowing cheaper and more diverse data collection. In a MoTR trial participants are presented with text that is blurred, except for a small in-focus region around the tip of the mouse. Participants move the mouse over the text, bringing individual words into focus in order to read. Mouse move- ment is recorded, and can be analyzed similarly to eye-tracking data. To facilitate MoTR experiments, we leverage the powerful Magpie framework designed for build- ing psychological online experiments. We validate it in two suites of experiments. First, we record MoTR data for the Provo Corpus (Luke and Christianson, 2018), for which eye-tracking data exists for comparison. We find strong correlations be- tween eye-tracking and MoTR reading times (RTs) from 0.73-0.79. Following the analysis approaches similar to Smith and Levy (2013), we find a linear effect on MoTR RTs of by-word surprisal (estimated from GPT-2). Second, we conduct a cross-methodological replication of three studies following Witzel et al. (2012) and Boyce et al. (2020) who test preference for adverb and relative clause high vs. low attachment and NP vs. S coordination preference. MoTR RTs replicate previous self-paced reading and maze task results while also shedding new light on the role of regressions in processing these phenomena