Minimizing resources of sweeping and streaming string transducers

We consider minimization problems for natural parameters of word transducers: the number of passes performed by two-way transducers and the number of registers used by streaming transducers. We show how to compute in ExpSpace the minimum number of passes needed to implement a transduction given as sweeping transducer, and we provide effective constructions of transducers of (worst-case optimal) doubly exponential size. We then consider streaming transducers where concatenations of registers are forbidden in the register updates. Based on a correspondence between the number of passes of sweeping transducers and the number of registers of equivalent concatenation-free streaming transducers, we derive a minimization procedure for the number of registers of concatenation-free streaming transducers

One-way definability of two-way word transducers

Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of `regular' mappings from words to words. It was shown in 2013 that it is decidable if such a transduction can be implemented by some one-way transducer, but the given algorithm has non-elementary complexity. We provide an algorithm of different flavor solving the above question, that has doubly exponential space complexity. In the special case of sweeping transducers the complexity is one exponential less. We also show how to construct an equivalent one-way transducer, whenever it exists, in doubly or triply exponential time, again depending on whether the input transducer is sweeping or two-way. In the sweeping case our construction is shown to be optimal

Re-pairing brackets

Consider the following one-player game. Take a well-formed sequence of opening and closing brackets (a Dyck word). As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the entire sequence, and the cost of a strategy is measured by its width: the maximum number of nonempty segments of symbols (separated by blank space) seen during the play. For various initial sequences, we prove upper and lower bounds on the minimum width sufficient for re-pairing. (In particular, the sequence associated with the complete binary tree of height n admits a strategy of width sub-exponential in log n.) Our two key contributions are (1) lower bounds on the width and (2) their application in automata theory: quasi-polynomial lower bounds on the translation from one-counter automata to Parikh-equivalent nondeterministic finite automata. The latter result answers a question by Atig et al. (2016)

REAL-TIME 4D ULTRASOUND RECONSTRUCTION FOR IMAGE-GUIDED INTRACARDIAC INTERVENTIONS

Image-guided therapy addresses the lack of direct vision associated with minimally- invasive interventions performed on the beating heart, but requires effective intraoperative imaging. Gated 4D ultrasound reconstruction using a tracked 2D probe generates a time-series of 3D images representing the beating heart over the cardiac cycle. These images have a relatively high spatial resolution and wide field of view, and ultrasound is easily integrated into the intraoperative environment. This thesis presents a real-time 4D ultrasound reconstruction system incorporated within an augmented reality environment for surgical guidance, whose incremental visualization reduces common acquisition errors. The resulting 4D ultrasound datasets are intended for visualization or registration to preoperative images. A human factors experiment demonstrates the advantages of real-time ultrasound reconstruction, and accuracy assessments performed both with a dynamic phantom and intraoperatively reveal RMS localization errors of 2.5-2.7 mm, and 0.8 mm, respectively. Finally, clinical applicability is demonstrated by both porcine and patient imaging

Journey 'Round the Sun: STEREO Science and Spacecraft Performance Results

The Solar TErrestrial RElations Observatory (STEREO) was originally designed as a two to five year heliocentric orbit mission to study coronal mass ejections (CMEs), solar energetic particles (SEPs), and the solar wind. After over ten years of continuous science data collection, the twin NASA STEREO observatories have significantly advanced the understanding of Heliophysics. This mission was the first to image CMEs all the way from the Sun to Earth and to observe the entire sphere of the Sun at one time. STEREO has demonstrated the importance of a point of view beyond the Sun-Earth line to significantly improve CME arrival time estimates and in understanding CME structure and trajectories and the longitudinal distribution of SEPs. STEREO was also the first to use one launch vehicle to insert two spacecraft into opposing heliocentric orbits, undergo a 3.5 month long superior solar conjunction, implement unattended daily science operations on two deep space observatories, maintain 7 arcsec continuous pointing without gyros, and detect and attempt to recover a spacecraft after a 22-month long communications anomaly at a range of 2 AU. This paper discusses the significant performance results after the first ten years of operations of the STEREO mission from its journey around the Sun

Journey 'Round the Sun: STEREO Science and Spacecraft Performance Results

The Solar TErrestrial RElations Observatory (STEREO) was originally designed as a two- to five-year heliocentric orbit mission to study coronal mass ejections (CMEs), solar energetic particles (SEPs), and the solar wind. After over ten years of continuous science data collection, the twin NASA STEREO observatories have significantly advanced the understanding of Heliophysics. This mission was the first to image CMEs all the way from the Sun to Earth and to observe the entire sphere of the Sun at one time. STEREO has demonstrated the importance of a point of view beyond the Sun-Earth line to significantly improve CME arrival time estimates and in understanding CME structure and trajectories and the longitudinal distribution of SEPs. STEREO was also the first to use one launch vehicle to insert two spacecraft into opposing heliocentric orbits, undergo a 3.5-month-long superior solar conjunction, implement unattended daily science operations on two deep space observatories, maintain 7 arcsec continuous pointing without gyros, and detect and attempt to recover a spacecraft after a 22-month long communications anomaly at a range of 2 AU (Astronomical Units). This paper discusses the significant performance results after the first ten years of operations of the STEREO mission from its journey around the Sun