Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functions

Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning kernel functions that approximate a fixed positive-pair kernel. We then prove that a simple representation obtained by combining this kernel with PCA provably minimizes the worst-case approximation error of linear predictors, under a straightforward assumption that positive pairs have similar labels. Our analysis is based on a decomposition of the target function in terms of the eigenfunctions of a positive-pair Markov chain, and a surprising equivalence between these eigenfunctions and the output of Kernel PCA. We give generalization bounds for downstream linear prediction using our Kernel PCA representation, and show empirically on a set of synthetic tasks that applying Kernel PCA to contrastive learning models can indeed approximately recover the Markov chain eigenfunctions, although the accuracy depends on the kernel parameterization as well as on the augmentation strength.Comment: Published at ICLR 202

Warm and fertile sub-humid conditions enhance litterfall to sustain high soil respiration fluxes in a mediterranean cork oak forest

Soil respiration is a major component of the global carbon budget and Mediterranean ecosystems have usually been studied in locations with shallow soils, mild temperatures, and a prolonged dry season. This study investigates seasonal soil respiration rates and underlying mechanisms under wetter, warmer, and more fertile conditions in a Mediterranean cork oak forest of Northern Tunisia (Africa), acknowledged as one of the most productive forests in the Mediterranean basin. We applied a soil respiration model based on soil temperature and relative water content and investigated how ecosystem functioning under these favorable conditions affected soil carbon storage through carbon inputs to the soil litter. Annual soil respiration rates varied between 1774 gC m(-2) year(-1) and 2227 gC m(-2) year(-1), which is on the highest range of observations under Mediterranean climate conditions. We attributed this high soil carbon flux as a response to favorable temperatures and soil water content, but this could be sustained only by a small carbon allocation to roots (root/shoot ratio = 0.31-0.41) leading to a large allocation to leaves with a multiannual leaf production, enhanced annual twig elongation (11.5-28.5 cm) with a reduced leaf life span (<1 year) maintaining a low LAI (1.68-1.88) and generating a high litterfall (386-636 gC m(-2) year(-1)). Thus, the favorable climatic and edaphic conditions experienced by these Mediterranean cork oak forests drove high soil respiration fluxes which balanced the high carbon assimilation leading to a relatively small overall contribution (10.96-14.79 kgC m(-2)) to soil carbon storage

Métodos alternativos de muestreo para estimar la estructura y caracteres reproductivos de bosques

Aleppo pine had a large forest cover in North Africa and along the Mediterranean basin which management is not fully developed and new forest tools are required. In this research, the forest structure, epidometric characteristics and allometric relationships were studied in 79 plots covering four bioclimatic zones from natural even aged forests of Aleppo pine located between eastern Algeria to the western coastal part of Tunisia. To characterize the forest structure three sampling methods were carried out: classical inventories (recording all pine trees), and two simplified approach using one average size or five dominant pine tree per plot. Annual growth increment and cone production were only calculated for the average size tree. Furthermore, the analysis of variance showed non-significant differences recorded between bioclimatic zones in trunk or crown diameter using the two simplified approach. Moreover, a significant decrease from wetter to drier areas in total height, crown height, cone seed production was observed only for average size tree method. However, the analysis of covariance showed significant differences between both approaches in total height, trunk diameter and crown coverage which were largely influenced by the pine tree density. In future investigations, we confirmed previous research that the dominant tree is a good sampling method to examine the site fertility, whereas the average size tree constitutes a valuable approach to study the population growth and reproduction.El pino carrasco muestra una gran cobertura forestal, tanto en el norte de África como en toda la Cuenca Mediterránea, cuyo manejo no está totalmente desarrollado lo que requiere nuevas herramientas de manejo. En esta investigación, se estudiaron la estructura forestal, las características epidométricas y las relaciones alométricas de 79 parcelas distribuidas a lo largo de cuatro zonas bioclimáticas en bosques regulares de pino carrasco situados entre el este de Argelia y la costa este de Túnez. Para caracterizar la estructura forestal se aplicaron tres métodos de muestreo: inventario clásico (midiendo todos los pies) y dos propuestas más sencillas, usando un árbol medio o cinco pies dominantes por parcela. El análisis de varianza no mostraba diferencias significativas de las mediciones de diámetro de tronco y de copa realizadas entre las distintas zonas bioclimáticas usando ambos métodos. Por otra parte, se observó una disminución significativa de las zonas más húmedas a las más secas en altura toral, altura de copa y producción de semillas fue observada aplicando el método de árbol medio. Además, el análisis de covarianzas mostraba diferencias significativas, usando ambas metodologías, en los valores medios de altura total, diámetro de tronco y cobertura de copa que mostraron estar influenciados por los valores de la densidad de arbolado de cada zona. Para futuras investigaciones, confirmamos estudios previos que apuntaban que la propuesta de muestreo de árboles dominantes como un buen método de muestreo para caracterizar la calidad de sitio mientras que la de árbol medio constituye una valiosa propuesta para el estudio del crecimiento de poblaciones y sus características reproductivas

Wear Process Description Based on Acoustic Emission

Since acoustic emissions are generated by fundamental mechanical processes, they can provide insight into the basic processes which determine friction and wear behavior. Descriptions Introduction When the mechanical state of a material body changes, energy is released, and some of it goes into the formation of transient stress waves called acoustic emission (AE). The surface displacements that occur when the AE interact with material surfaces are easy to measure using a displacement sensor mounted on the surface. These measurements provide a signal related to the AE and hence to the physical process which generated it. The ease of AE measurements and the possibility of relating them to the fundamental mechanical processes of deformation, fracture, and structural and compositional changes are strong incentives for the use of AE monitoring in material behavior characterization. In the tribological setting, AE measurements have two general uses. One is in basic studies of the mechanical processes giving rise to friction and wear. The goal is to relate signal characteristics to basic mechanical processes and so gain a detailed understanding of friction and wear. Another general use of AE monitoring is in the continuous assessment of material and machinery states. Material and interface monitoring is useful for performance measurement and condition monitoring. Two difficulties arise in AE monitoring. In almost all applications, the AE generation site and sensor location are widely separated. The transmission of the AE through the intervening material results in attenuation and, in extreme cases, such as transmission through material interfaces, in a change in form of the AE. More specific to tribological studies are complications in AE signal interpretation which may arise due to the high AE generation rates expected. Typically, friction and wear occur over an extended volume, and the rates of the processes are high. The result is that the individual transient stress waves generated interact with a large number of other AE and lose their distinct identity and characteristics. Signal interpretation then becomes a problem