Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Alternative derivation of the relativistic contribution to perihelic precession

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal of Physic

Expected-value bias in routine third-trimester growth scans.

OBJECTIVES: Operators performing fetal growth scans are usually aware of the gestational age of the pregnancy, which may lead to expected-value bias when performing biometric measurements. We aimed to evaluate the incidence of expected-value bias in routine fetal growth scans and assess its impact on standard biometric measurements. METHODS: We collected prospectively full-length video recordings of routine ultrasound growth scans coupled with operator eye tracking. Expected value was defined as the gestational age at the time of the scan, based on the estimated due date that was established at the dating scan. Expected-value bias was defined as occurring when the operator looked at the measurement box on the screen during the process of caliper adjustment before saving a measurement. We studied the three standard biometric planes on which measurements of head circumference (HC), abdominal circumference (AC) and femur length (FL) are obtained. We evaluated the incidence of expected-value bias and quantified the impact of biased measurements. RESULTS: We analyzed 272 third-trimester growth scans, performed by 16 operators, during which a total of 1409 measurements (354 HC, 703 AC and 352 FL; including repeat measurements) were obtained. Expected-value bias occurred in 91.4% of the saved standard biometric plane measurements (85.0% for HC, 92.9% for AC and 94.9% for FL). The operators were more likely to adjust the measurements towards the expected value than away from it (47.7% vs 19.7% of measurements; P < 0.001). On average, measurements were corrected by 2.3 ± 5.6, 2.4 ± 10.4 and 3.2 ± 10.4 days of gestation towards the expected gestational age for the HC, AC, and FL measurements, respectively. Additionally, we noted a statistically significant reduction in measurement variance once the operator was biased (P = 0.026). Comparing the lowest and highest possible estimated fetal weight (using the smallest and largest biased HC, AC and FL measurements), we noted that the discordance, in percentage terms, was 10.1% ± 6.5%, and that in 17% (95% CI, 12-21%) of the scans, the fetus could be considered as small-for-gestational age or appropriate-for-gestational age if using the smallest or largest possible measurements, respectively. Similarly, in 13% (95% CI, 9-16%) of scans, the fetus could be considered as large-for-gestational age or appropriate-for-gestational age if using the largest or smallest possible measurements, respectively. CONCLUSIONS: During routine third-trimester growth scans, expected-value bias frequently occurs and significantly changes standard biometric measurements obtained. © 2019 the Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of the International Society of Ultrasound in Obstetrics and Gynecology

Universal homogeneous causal sets

Causal sets are particular partially ordered sets which have been proposed as a basic model for discrete space-time in quantum gravity. We show that the class C of all countable past-finite causal sets contains a unique causal set (U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can be constructed both probabilistically and explicitly. In contrast, the larger class of all countable causal sets does not contain a universal object.Comment: 14 page

Mean-payoff Automaton Expressions

Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic mean-payoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions

The use of embolic signal detection in multicenter trials to evaluate antiplatelet efficacy: signal analysis and quality control mechanisms in the CARESS (Clopidogrel and Aspirin for Reduction of Emboli in Symptomatic carotid Stenosis) trial

&lt;p&gt;&lt;b&gt;Background and Purpose:&lt;/b&gt; The CARESS (Clopidogrel and Aspirin for Reduction of Emboli in Symptomatic carotid Stenosis) trial proved the effectiveness of the combination of clopidogrel and aspirin compared with aspirin alone in reducing presence and number of microembolic signals (MES) in patients with recently symptomatic carotid stenosis. The present study aimed at installing primary and secondary quality control measures in CARESS because MES evaluation relies on subjective judgment by human experts.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; As primary quality control, centers participating in CARESS evaluated a reference digital audio tape (DAT) before the study containing both MES and artifacts. Interobserver agreement of classifying signals as MES was expressed as proportions of specific agreement of positive ratings (ps±values). For all DATs included in CARESS (n=300), online number of MES and off-line number of MES read by the central reader were compared using correlation coefficients. As secondary control, a sample of 16 of 300 DATs was cross-validated by another independent reader (post-trial validator).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; For the reference tape, the cumulative ps±value was 0.894 based on 12 of 14 observers. Two observers with very different results improved after a training procedure. Agreement between post-trial validator and central reader was ps+=0.805, indicating very good agreement. Correlation between online evaluation and off-line evaluation of DATs was very good overall (cumulative ρ=0.84; P&#60;0.001).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusion:&lt;/b&gt; Multicenter studies using MES as outcome parameter are feasible. However, primary and secondary quality control procedures are important.&lt;/p&gt

Optical Frequency Comb Generation based on Erbium Fiber Lasers

Citation: Droste, S., Ycas, G., Washburn, B. R., Coddington, I., & Newbury, N. R. (2016). Optical Frequency Comb Generation based on Erbium Fiber Lasers. Nanophotonics, 5(2), 196-213. doi:10.1515/nanoph-2016-0019Optical frequency combs have revolutionized optical frequency metrology and are being actively investigated in a number of applications outside of pure optical frequency metrology. For reasons of cost, robustness, performance, and flexibility, the erbium fiber laser frequency comb has emerged as the most commonly used frequency comb system and many different designs of erbium fiber frequency combs have been demonstrated. We review the different approaches taken in the design of erbium fiber frequency combs, including the major building blocks of the underlying mode-locked laser, amplifier, supercontinuum generation and actuators for stabilization of the frequency comb

Spatio-Temporal Partitioning And Description Of Full-Length Routine Fetal Anomaly Ultrasound Scans

This paper considers automatic clinical workflow description of full-length routine fetal anomaly ultrasound scans using deep learning approaches for spatio-temporal video analysis. Multiple architectures consisting of 2D and 2D + t CNN, LSTM, and convolutional LSTM are investigated and compared. The contributions of short-term and long-term temporal changes are studied, and a multi-stream framework analysis is found to achieve the best top-l accuracy =0.77 and top-3 accuracy =0.94. Automated partitioning and characterisation on unlabelled full-length video scans show high correlation (ρ=0.95, p=0.0004) with workflow statistics of manually labelled videos, suggesting practicality of proposed methods

Near-Optimal Scheduling for LTL with Future Discounting

We study the search problem for optimal schedulers for the linear temporal logic (LTL) with future discounting. The logic, introduced by Almagor, Boker and Kupferman, is a quantitative variant of LTL in which an event in the far future has only discounted contribution to a truth value (that is a real number in the unit interval [0, 1]). The precise problem we study---it naturally arises e.g. in search for a scheduler that recovers from an internal error state as soon as possible---is the following: given a Kripke frame, a formula and a number in [0, 1] called a margin, find a path of the Kripke frame that is optimal with respect to the formula up to the prescribed margin (a truly optimal path may not exist). We present an algorithm for the problem; it works even in the extended setting with propositional quality operators, a setting where (threshold) model-checking is known to be undecidable