On nef and semistable hermitian lattices, and their behaviour under tensor product

We study the behaviour of semistability under tensor product in various settings: vector bundles, euclidean and hermitian lattices (alias Humbert forms or Arakelov bundles), multifiltered vector spaces. One approach to show that semistable vector bundles in characteristic zero are preserved by tensor product is based on the notion of nef vector bundles. We revisit this approach and show how far it can be transferred to hermitian lattices. J.-B. Bost conjectured that semistable hermitian lattices are preserved by tensor product. Using properties of nef hermitian lattices, we establish an inequality which improves on earlier results in that direction. On the other hand, we show that, in contrast to nef vector bundles, nef hermitian lattices are not preserved by tensor product. We axiomatize our method in the general context of monoidal categories, and give an elementary proof of the fact that semistable multifiltered vector spaces (which play a role in diophantine approximation) are preserved by tensor product.Comment: revised versio

On frequency and time domain models of traveling wave tubes

We discuss the envelope modulation assumption of frequency-domain models of traveling wave tubes (TWTs) and test its consistency with the Maxwell equations. We compare the predictions of usual frequency-domain models with those of a new time domain model of the TWT

The influence of problem features and individual differences on strategic performance in simple arithmetic

The present study examined the influence of features differing across problems (problem size and operation) and differing across individuals (daily arithmetic practice, the amount of calculator use, arithmetic skill, and gender) on simple-arithmetic performance. Regression analyses were used to investigate the role of these variables in both strategy selection and strategy efficiency. Results showed that more-skilled and highly practiced students used memory retrieval more often and executed their strategies more efficiently than less-skilled and less practiced students. Furthermore, calculator use was correlated with retrieval efficiency and procedural efficiency but not with strategy selection. Only very small associations with gender were observed, with boys retrieving slightly faster than girls. Implications of the present findings for views on models of mental arithmetic are discussed

Parametric modeling of photometric signals

This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The Cramér Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The Neyman–Pearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The Neyman–Pearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations

Cramer–Rao lower bounds for change points in additive and multiplicative noise

The paper addresses the problem of determining the Cramer–Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are first derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs corresponding to this model are shown to be well approximated by the more tractable expressions derived for a known change-point. The paper also shows that the step location parameter is asymptotically decoupled from the other parameters, which allows us to derive simple CRLBs for the step location. These bounds are then compared with the corresponding mean square errors of the maximum likelihood estimators in the pure multiplicative case. The comparison illustrates convergence and efficiency of the ML estimator. An extension to colored multiplicative noise is also discussed