Characteristic Laplacian in sub-Riemannian geometry

We study a Laplacian operator related to the characteristic cohomology of a smooth manifold endowed with a distribution. We prove that this Laplacian does not behave very well: it is not hypoelliptic in general and does not respect the bigrading on forms in a complex setting. We also discuss the consequences of these negative results for a conjecture of P. Griffiths, concerning the characteristic cohomology of period domains

Layout of Multiple Views for Volume Visualization: A User Study

Abstract. Volume visualizations can have drastically different appearances when viewed using a variety of transfer functions. A problem then occurs in trying to organize many different views on one screen. We conducted a user study of four layout techniques for these multiple views. We timed participants as they separated different aspects of volume data for both time-invariant and time-variant data using one of four different layout schemes. The layout technique had no impact on performance when used with time-invariant data. With time-variant data, however, the multiple view layouts all resulted in better times than did a single view interface. Surprisingly, different layout techniques for multiple views resulted in no noticeable difference in user performance. In this paper, we describe our study and present the results, which could be used in the design of future volume visualization software to improve the productivity of the scientists who use it

Changing preferences: an experiment and estimation of market-incentive effects on altruism

This paper studies how altruistic preferences are changed by markets and incentives. We conduct a laboratory experiment in a within-subject design. Subjects are asked to choose health care qualities for hypothetical patients in monopoly, duopoly, and quadropoly. Prices, costs, and patient benefits are experimental incentive parameters. In monopoly, subjects choose quality to tradeoff between profits and altruistic patient benefits. In duopoly and quadropoly, we model subjects playing a simultaneous-move game. Each subject is uncertain about an opponent's altruism, and competes for patients by choosing qualities. Bayes-Nash equilibria describe subjects' quality decisions as functions of altruism. Using a nonparametric method, we estimate the population altruism distributions from Bayes-Nash equilibrium qualities in different markets and incentive configurations. Markets tend to reduce altruism, although duopoly and quadropoly equilibrium qualities are much higher than those in monopoly. Although markets crowd out altruism, the disciplinary powers of market competition are stronger. Counterfactuals confirm markets change preferences.Accepted manuscrip

Accuracy-based scoring for phrase-based statistical machine translation

Although the scoring features of state-of-the-art Phrase-Based Statistical Machine Translation (PB-SMT) models are weighted so as to optimise an objective function measuring translation quality, the estimation of the features themselves does not have any relation to such quality metrics. In this paper, we introduce a translation quality-based feature to PBSMT in a bid to improve the translation quality of the system. Our feature is estimated by averaging the edit-distance between phrase pairs involved in the translation of oracle sentences, chosen by automatic evaluation metrics from the N-best outputs of a baseline system, and phrase pairs occurring in the N-best list. Using our method, we report a statistically significant 2.11% relative improvement in BLEU score for the WMT 2009 Spanish-to-English translation task. We also report that using our method we can achieve statistically significant improvements over the baseline using many other MT evaluation metrics, and a substantial increase in speed and reduction in memory use (due to a reduction in phrase-table size of 87%) while maintaining significant gains in translation quality

Reconciling modern machine learning practice and the bias-variance trade-off

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning

Anytime Control using Input Sequences with Markovian Processor Availability

We study an anytime control algorithm for situations where the processing resources available for control are time-varying in an a priori unknown fashion. Thus, at times, processing resources are insufficient to calculate control inputs. To address this issue, the algorithm calculates sequences of tentative future control inputs whenever possible, which are then buffered for possible future use. We assume that the processor availability is correlated so that the number of control inputs calculated at any time step is described by a Markov chain. Using a Lyapunov function based approach we derive sufficient conditions for stochastic stability of the closed loop.Comment: IEEE Transactions on Automatic Control, to be publishe