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Preventing humans from committing errors is a crucial aspect of man-machine interaction and systems of computer assistance. It is a basic implication that those systems need to recognise errors before they occur. This paper reports an exploratory study that utilises eye-tracking technology and automated face recognition in order to analyse test persons' emotional reactions and cognitive load during a computer game and learning through trial and error. Computer algorithms based on machine learning and big data were tested that identify particular patterns of test persons' gaze behaviour and facial expressions that antecede errors in a computer game. The results show that emotions and learning from errors are positively correlated and that gaze behaviour and facial expressions inform about the errors that follow. However, the algorithms still need to be improved through further studies to be suitable for daily use. This research is innovative in its use of mathematical formulae to operationalise learning through errors and the use of computer algorithms to predict errors in human behaviour in trial-and-error situations.

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran's well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator. Key words: forest inventory, permanent plots, two-phase sampling for stratification, bootstrap resampling, variance decomposition. Le double echantillonnage stratifie (2ES) est un plan d'echantillonnage largement utilise pour les inventaires forestiers. Nous presentons deux estimateurs de variance, qui conviennent a la croissance moyenne, derives mathematiquement a partir du 2ES repete avec une stratification mise a jour a chaque mesure. Les deux estimateurs tiennent compte de la sousstratification basee sur la transition des unites d'echantillonnage entre les strates en raison de la mise a jour de l'allocation. Pour le premier estimateur, la taille des sous-strates a ete estimee a partir de l'echantillon de la deuxieme phase (placettes d'echantillonnage), tandis que la taille des sous-strates respectives pour le deuxieme estimateur de la variance reposait sur l'echantillon plus grand de la premiere phase. Les estimateurs ont ete compares empiriquement a une version modifiee de l'estimateur de variance 2ES bien connu de Cochran qui ignore la sous-stratification. Cela a ete fait en effectuant un reechantillonnage multiple dans les donnees de deux districts forestiers allemands. Les principales conclusions etaient les suivantes: (i) la prise en compte de la sous-stratification, telle qu'elle est mise en reuvre dans les deux nouveaux estimateurs, a un impact substantiel en termes d'estimation de la variance et de du biais, qui sont significativement plus faibles par rapport a l'estimateur sans sous-stratification, et (ii) le deuxieme estimateur, dont la taille des sous-strates est estimee a partir de l'echantillon de la premiere phase, montre un biais plus petit que le premier estimateur. [Traduit par la Redaction] Mots-cles : inventaire forestier, placettes permanentes, double echantillonnage stratifie, reechantillonnage multiple, decomposition de la variance., 1. Introduction Double sampling for stratification (2SS) is a basic technique in forest inventory and is accordingly treated in all standard textbooks (deVries 1986; Schreuder et al. 1993; Gregoire and [...]

Tropical Africa and the North Atlantic Ocean are significantly influenced by African easterly waves (AEWs), which play a fundamental role in tropical rainfall and cyclogenesis in that region. The dynamics of AEWs can be described in a potential vorticity (PV) framework. The important impact of latent heat release by cloud processes is captured in this framework by the diabatic generation of PV anomalies. This paper introduces an innovative approach for the identification and tracking of PV structures within AEWs. By employing AEW tracking and computing the wave phase of each point within the AEW domain using a Hilbert transform, we are able to effectively identify and collect 3-D PV structures associated with specific AEWs. To facilitate a climatological analysis, performed here over the months of June to October from 2002 to 2022, these structures are subsequently characterized by low-dimensional descriptors, including their location, intensity, and orientation. Our climatological analysis reveals the seasonal evolution and the structural attributes of PV anomalies within AEWs over the study domain. PV feature locations closely align with the African easterly jet's latitudinal shift during the summer season. Analysis of the mean pressure level of the 3-D PV structures shows a remarkable shift during their life cycle, indicating deep moist convection characteristics over land and more shallow convection characteristics over the ocean. On average, PV features identified within AEW troughs tilt downshear over land and equatorward over the ocean. The trough-centered analysis reveals distinct differences between satellite-estimated and model-predicted rainfall. Agreement between the results of a more traditional composite analysis and our new feature analysis provides confidence in our feature approach as a novel diagnostic tool. The feature framework provides a low-dimensional representation of the PV structure of AEWs, which facilitates future statistical analyses of the relation of this structure to, for example, tropical cyclogenesis or the predictability of tropical rainfall. [ABSTRACT FROM AUTHOR]

Volume growth is a key indicator in forest management and planning and, accordingly, an integral part of the estimation procedure of forest resources from sample based inventories. Growth estimation from successive double sampling for stratification (2SS) is somewhat challenging and has not been sufficiently addressed in the pertinent literature. Applying 2SS on successive occasions, with updated stratification on each occasion, may lead to fluctuation of samplingunits among the strata and to a certain number of sample plots that have to be discarded or that have to be newly established on the second occasion, to obtain the required per-strata sampling proportions, which are stipulated in advance. After presenting a notation to implement growth estimation into 2SS standard formulas, the question of strata shifts and the occurrence of discarded and of new sample plots in the context of growth estimation is addressed. Although growth, unlike net change, can only be estimated from direct observations on remeasured sample plots, it was shown that ignoring discarded or new plots might lead to severely biased estimators. Modified estimators for mean growth and variances are provided and their application is illustrated using data from a repeated survey in a central German forest district. Key words: continuous forest inventory, growth components, permanent plot, two-phase sampling. La croissance en volume est un indicateur cle pour la planification et la gestion des forets et, par consequent, un element essentiel de la procedure d'estimation des ressources forestieres au moyen d'un inventaire par echantillonnage. L'estimation de la croissance a partir d'un echantillonnage stratifie a deux degres successifs (2DS) pose un defi et n'a pas ete suffisamment abordee dans la litterature pertinente. L'application successive de 2DS, avec une stratification mise a jour a chaque fois, peut entramer une fluctuation des unites d'echantillonnage au sein des strates; il est possible qu'un certain nombre de placettes-echantillons doivent etre eliminees ou nouvellement etablies a la deuxieme occasion afin d'atteindre les proportions requises d'echantillons par strate, qui sont stipulees a l'avance. Apres avoir presente une notation pour accomplir l'estimation de la croissance avec les formules standards 2DS, la question de la fluctuation des strates et de l'occurrence de placettes ecartees et ajoutees a l'echantillonnage est abordee. Bien que la croissance, contrairement au changement net, ne puisse etre estimee qu'a partir d'observations directes sur des placettes-echantillons remesurees, il a ete demontre que le fait d'ignorer les placettes ecartees ou nouvelles risquait d'engendrer des estimateurs extremement biaises. Des estimateurs modifies de la croissance moyenne et des variances sont fournis et leur application est illustree a l'aide des donnees d'une enquete en mesures repetees menee dans un district forestier du centre de l'Allemagne. [Traduit par la Redaction] Mots-cles: inventaire forestier continu, composantes de la croissance, placette-echantillon permanente, echantillonnage a deux degres., 1. Introduction Due to its efficiency, double sampling for stratification (2SS) is a basic technique in forest inventory and is treated in all standard textbooks (de Vries 1986; Schreuder et [...]