Probabilistic Analysis of Optimization Problems on Generalized Random Shortest Path Metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics on complete graphs to analyze heuristics. The goal of this paper is to generalize these findings to non-complete graphs, especially Erd\H{o}s-R\'enyi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the $k$-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.Comment: An extended abstract appeared in the proceedings of WALCOM 201

Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

Reinstated episodic context guides sampling-based decisions for reward.

How does experience inform decisions? In episodic sampling, decisions are guided by a few episodic memories of past choices. This process can yield choice patterns similar to model-free reinforcement learning; however, samples can vary from trial to trial, causing decisions to vary. Here we show that context retrieved during episodic sampling can cause choice behavior to deviate sharply from the predictions of reinforcement learning. Specifically, we show that, when a given memory is sampled, choices (in the present) are influenced by the properties of other decisions made in the same context as the sampled event. This effect is mediated by fMRI measures of context retrieval on each trial, suggesting a mechanism whereby cues trigger retrieval of context, which then triggers retrieval of other decisions from that context. This result establishes a new avenue by which experience can guide choice and, as such, has broad implications for the study of decisions

Frequency-Dependent Properties of a Fluid Jet Stimulus: Calibration, Modeling, and Application to Cochlear Hair Cell Bundles

The investigation of small physiological mechano-sensory systems, such as hair cells or their accessory structures in the inner ear or lateral line organ, requires mechanical stimulus equipment that allows spatial manipulation with micrometer precision and stimulation with amplitudes down to the nanometer scale. Here, we describe the calibration of a microfluid jet produced by a device that was designed to excite individual cochlear hair cell bundles or cupulae of the fish superficial lateral line system. The calibration involves a precise definition of the linearity and time- and frequency-dependent characteristics of the fluid jet as produced by a pressurized fluid-filled container combined with a glass pipette having a microscopically sized tip acting as an orifice. A procedure is described that can be applied during experiments to obtain a fluid jet’s frequency response, which may vary with each individual glass pipette. At small orifice diameters (<15 μm), the fluid velocity of the jet is proportional to the displacement of the piezoelectric actuator pressurizing the container’s volume and is suitable to stimulate the hair bundles of sensory hair cells. With increasing diameter, the fluid jet velocity becomes proportional to the actuator’s velocity. The experimentally observed characteristics can be described adequately by a dynamical model of damped fluid masses coupled by elastic components

Steps in the bacterial flagellar motor

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps [Sowa et al. (2005) Nature 437, 916--919]. Here we propose a simple physical model that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties, and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. Our model also predicts a sublinear torque-speed relationship at low torque, and a peak in rotor diffusion as a function of torque

PACE-UP (Pedometer and consultation evaluation--UP)--a pedometer-based walking intervention with and without practice nurse support in primary care patients aged 45-75 years: study protocol for a randomised controlled trial.

BACKGROUND: Most adults do not achieve the 150 minutes weekly of at least moderate intensity activity recommended for health. Adults' most common physical activity (PA) is walking, light intensity if strolling, moderate if brisker. Pedometers can increase walking; however, most trials have been short-term, have combined pedometer and support effects, and have not reported PA intensity. This trial will investigate whether pedometers, with or without nurse support, can help less active 45-75 year olds to increase their PA over 12 months. METHODS/DESIGN: DESIGN: Primary care-based 3-arm randomized controlled trial with 12-month follow-up and health economic and qualitative evaluations. PARTICIPANTS: Less active 45-75 year olds (n = 993) will be recruited by post from six South West London general practices, maximum of two per household and households randomised into three groups. Step-count and time spent at different PA intensities will be assessed for 7 days at baseline, 3 and 12 months by accelerometer. Questionnaires and anthropometric assessments will be completed. INTERVENTION: The pedometer-alone group will be posted a pedometer (Yamax Digi-Walker SW-200), handbook and diary detailing a 12-week pedometer-based walking programme, using targets from their baseline assessment. The pedometer-plus-support group will additionally receive three practice nurse PA consultations. The handbook, diary and consultations include behaviour change techniques (e.g., self-monitoring, goal-setting, relapse prevention planning). The control group will receive usual care. OUTCOMES: Changes in average daily step-count (primary outcome), time spent sedentary and in at least moderate intensity PA weekly at 12 months, measured by accelerometry. Other outcomes include change in body mass index, body fat, self-reported PA, quality of life, mood and adverse events. Cost-effectiveness will be assessed by the incremental cost of the intervention to the National Health Service and incremental cost per change in step-count and per quality adjusted life year. Qualitative evaluations will explore reasons for trial non-participation and the interventions' acceptability. DISCUSSION: The PACE-UP trial will determine the effectiveness and cost-effectiveness of a pedometer-based walking intervention delivered by post or practice nurse to less active primary care patients aged 45-75 years old. Approaches to minimise bias and challenges anticipated in delivery will be discussed

Direct Detection of Hydrogen Bonds in Supramolecular Systems Using ¹H–¹⁵N Heteronuclear Multiple Quantum Coherence Spectroscopy

Hydrogen-bonded supramolecular systems are usually characterized in solution through analysis of NMR data such as complexation-induced shifts and nuclear Overhauser effects (nOe). Routine direct detection of hydrogen bonding particularly in multicomponent mixtures, even with the aid of 2D NMR experiments for full assignment, is more challenging. We describe an elementary rapid 1H–15N HMQC NMR experiment which addresses these challenges without the need for complex pulse sequences. Under readily accessible conditions (243/263 K, 50 mM solutions) and natural 15N abundance, unambiguous assignment of 15N resonances facilitates direct detection of intra- and intermolecular hydrogen bonds in mechanically interlocked structures and quadruply hydrogen-bonded dimers─of dialkylaminoureidopyrimidinones, ureidopyrimidinones, and diamidonaphthyridines─in single or multicomponent mixtures to establish tautomeric configuration, conformation, and, to resolve self-sorted speciation

Scientists Want More Children

Scholars partly attribute the low number of women in academic science to the impact of the science career on family life. Yet, the picture of how men and women in science – at different points in the career trajectory – compare in their perceptions of this impact is incomplete. In particular, we know little about the perceptions and experiences of junior and senior scientists at top universities, institutions that have a disproportionate influence on science, science policy, and the next generation of scientists. Here we show that having fewer children than wished as a result of the science career affects the life satisfaction of science faculty and indirectly affects career satisfaction, and that young scientists (graduate students and postdoctoral fellows) who have had fewer children than wished are more likely to plan to exit science entirely. We also show that the impact of science on family life is not just a woman's problem; the effect on life satisfaction of having fewer children than desired is more pronounced for male than female faculty, with life satisfaction strongly related to career satisfaction. And, in contrast to other research, gender differences among graduate students and postdoctoral fellows disappear. Family factors impede talented young scientists of both sexes from persisting to research positions in academic science. In an era when the global competitiveness of US science is at risk, it is concerning that a significant proportion of men and women trained in the select few spots available at top US research universities are considering leaving science and that such desires to leave are related to the impact of the science career on family life. Results from our study may inform university family leave policies for science departments as well as mentoring programs in the sciences