Laryngeal split and rib cartilage interpositional grafting: Treatment option for glottic/subglottic stenosis in adults

Objectives: Severe glottic/subglottic stenosis (complex laryngotracheal stenosis) is a rare but challenging complication of endotracheal intubation. Laryngotracheal reconstruction with cartilage graft and an intralaryngeal stent is a procedure described for complex laryngotracheal stenosis management in children; however, for adults, few options remain. Our aim was to analyze the results of laryngotracheal reconstruction as a treatment for complex laryngotracheal stenosis in adults, considering postoperative and long-term outcome. Methods: Laryngotracheal reconstruction (laryngeal split with anterior and posterior interposition of a rib cartilage graft) has been used in our institution to manage glottic/subglottic stenosis restricted to the larynx; laryngotracheal reconstruction associated with cricotracheal resection has been used to treat glottic/subglottic/upper tracheal stenosis (extending beyond the second tracheal ring). A retrospective study was conducted, including all patients with complex laryngotracheal stenosis treated surgically in our institution from January of 2002 until December of 2005. Results: Twenty patients (10 male and 10 female patients; average age, 36.13 years; age range, 18-54 years) were included. There were no deaths, and the postoperative complications were as follows: dysphonia, 25%; subcutaneous emphysema, 10%; tracheocutaneous fistula, 20%; wound infection, 15%; and bleeding, 5.0%. Eighty percent of the patients were completely decannulated after a mean of 23.4 months of follow-up (range, 4 -55 months). Conclusions: Laryngeal split with anterior and posterior cartilage graft interposition as an isolated procedure or associated with a cricotracheal resection is a feasible and low-morbidity alternative for complex laryngotracheal stenosis treatment.

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Splitting rivers at their seams: bifurcations and avulsion

River bifurcations are critical but poorly understood elements of many geomorphological systems. They are integral elements of alluvial fans, braided rivers, fluvial lowland plains, and deltas and control the partitioning of water and sediment through these systems. Bifurcations are commonly unstable but their lifespan varies greatly. In braided rivers bars and channels migrate, split and merge at annual or shorter timescales, thereby creating and abandoning bifurcations. This behaviour has been studied mainly by geomorphologists and fluid dynamicists. Bifurcations also exist during avulsion, the process of a river changing course on a floodplain or in a delta, which may take 102103 years and has been studied mainly by sedimentologists. This review synthesizes our current understanding of bifurcations and brings together insights from different research communities and different environmental settings. We consider the causes and initiation of bifurcations and avulsion, the physical mechanisms controlling bifurcation and avulsion evolution, mathematical and numerical modelling of these processes, and the possibility of stable bifurcations. We end the review with some open questions. Copyright (c) 2012 John Wiley & Sons, Ltd.

Habitat split and the global decline of amphibians

The worldwide decline in amphibians has been attributed to several causes, especially habitat loss and disease. We identified a further factor, namely habitat split- defined as human- induced disconnection between habitats used by different life history stages of a species- which forces forest- associated amphibians with aquatic larvae to make risky breeding migrations between suitable aquatic and terrestrial habitats. In the Brazilian Atlantic Forest, we found that habitat split negatively affects the richness of species with aquatic larvae but not the richness of species with terrestrial development ( the latter can complete their life cycle inside forest remnants). This mechanism helps to explain why species with aquatic larvae have the highest incidence of population decline. These findings reinforce the need for the conservation and restoration of riparian vegetation.

Functional split and crosslinking of the membrane domain of the β subunit of proton-translocating transhydrogenase from Escherichia coli

Proton pumping nicotinamide nucleotide transhydrogenase from Escherichia coli contains an α subunit with the NAD(H)-binding domain I and a β subunit with the NADP(H)-binding domain III. The membrane domain (domain II) harbors the proton channel and is made up of the hydrophobic parts of the α and β subunits. The interface in domain II between the α and the β subunits has previously been investigated by cross-linking loops connecting the four transmembrane helices in the α subunit and loops connecting the nine transmembrane helices in the β subunit. However, to investigate the organization of the nine transmembrane helices in the β subunit, a split was introduced by creating a stop codon in the loop connecting transmembrane helices 9 and 10 by a single mutagenesis step, utilizing an existing downstream start codon. The resulting enzyme was composed of the wild-type α subunit and the two new peptides β1 and β2. As compared to other split membrane proteins, the new transhydrogenase was remarkably active and catalyzed activities for the reduction of 3-acetylpyridine-NAD + by NADPH, the cyclic reduction of 3-acetylpyridine-NAD + by NADH (mediated by bound NADP(H)), and proton pumping, amounting to about 50-107% of the corresponding wild-type activities. These high activities suggest that the α subunit was normally folded, followed by a concerted folding of β1 + β2. Cross-linking of a βS105C-βS237C double cysteine mutant in the functional split cysteine-free background, followed by SDS-PAGE analysis, showed that helices 9, 13, and 14 were in close proximity. This is the first time that cross-linking between helices in the same β subunit has been demonstrated.

Chain Split and Computations in Practical Rule Mining

A novel association rule mining algorithm is composed, using the unit cube chain decomposition structures introduced in [HAN, 1966; TON, 1976]. [HAN, 1966] established the chain split theory. [TON, 1976] invented an excellent chain computation framework which brings chain split into the practical domain. We integrate these technologies around the rule mining procedures. Effectiveness is related to the intention of low complexity of rules mined. Complexity of the procedure composed is complementary to the known Apriori algorithm which is defacto standard in rule mining area.

Methods for Region Based Paper Surface Roughness Measurement

Paperin pinnan karheus on yksi paperin laatukriteereistä. Sitä mitataan fyysisestipaperin pintaa mittaavien laitteiden ja optisten laitteiden avulla. Mittaukset vaativat laboratorioolosuhteita, mutta nopeammille, suoraan linjalla tapahtuville mittauksilla olisi tarvetta paperiteollisuudessa. Paperin pinnan karheus voidaan ilmaista yhtenä näytteelle kohdistuvana karheusarvona. Tässä työssä näyte on jaettu merkitseviin alueisiin, ja jokaiselle alueelle on laskettu erillinen karheusarvo. Karheuden mittaukseen on käytetty useita menetelmiä. Yleisesti hyväksyttyä tilastollista menetelmää on käytetty tässä työssä etäisyysmuunnoksen lisäksi. Paperin pinnan karheudenmittauksessa on ollut tarvetta jakaa analysoitava näyte karheuden perusteella alueisiin. Aluejaon avulla voidaan rajata näytteestä selvästi karheampana esiintyvät alueet. Etäisyysmuunnos tuottaa alueita, joita on analysoitu. Näistä alueista on muodostettu yhtenäisiä alueita erilaisilla segmentointimenetelmillä. PNN -menetelmään (Pairwise Nearest Neighbor) ja naapurialueiden yhdistämiseen perustuvia algoritmeja on käytetty.Alueiden jakamiseen ja yhdistämiseen perustuvaa lähestymistapaa on myös tarkasteltu. Segmentoitujen kuvien validointi on yleensä tapahtunut ihmisen tarkastelemana. Tämän työn lähestymistapa on verrata yleisesti hyväksyttyä tilastollista menetelmää segmentoinnin tuloksiin. Korkea korrelaatio näiden tulosten välillä osoittaa onnistunutta segmentointia. Eri kokeiden tuloksia on verrattu keskenään hypoteesin testauksella. Työssä on analysoitu kahta näytesarjaa, joidenmittaukset on suoritettu OptiTopolla ja profilometrillä. Etäisyysmuunnoksen aloitusparametrit, joita muutettiin kokeiden aikana, olivat aloituspisteiden määrä ja sijainti. Samat parametrimuutokset tehtiin kaikille algoritmeille, joita käytettiin alueiden yhdistämiseen. Etäisyysmuunnoksen jälkeen korrelaatio oli voimakkaampaa profilometrillä mitatuille näytteille kuin OptiTopolla mitatuille näytteille. Segmentoiduilla OptiTopo -näytteillä korrelaatio parantui voimakkaammin kuin profilometrinäytteillä. PNN -menetelmän tuottamilla tuloksilla korrelaatio oli paras.

Image Segmentation Using Information Bottleneck Method

In image processing, segmentation algorithms constitute one of the main focuses of research. In this paper, new image segmentation algorithms based on a hard version of the information bottleneck method are presented. The objective of this method is to extract a compact representation of a variable, considered the input, with minimal loss of mutual information with respect to another variable, considered the output. First, we introduce a split-and-merge algorithm based on the definition of an information channel between a set of regions (input) of the image and the intensity histogram bins (output). From this channel, the maximization of the mutual information gain is used to optimize the image partitioning. Then, the merging process of the regions obtained in the previous phase is carried out by minimizing the loss of mutual information. From the inversion of the above channel, we also present a new histogram clustering algorithm based on the minimization of the mutual information loss, where now the input variable represents the histogram bins and the output is given by the set of regions obtained from the above split-and-merge algorithm. Finally, we introduce two new clustering algorithms which show how the information bottleneck method can be applied to the registration channel obtained when two multimodal images are correctly aligned. Different experiments on 2-D and 3-D images show the behavior of the proposed algorithms

Simulation de centres de contacts

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Image Segmentation Using Information Bottleneck Method

In image processing, segmentation algorithms constitute one of the main focuses of research. In this paper, new image segmentation algorithms based on a hard version of the information bottleneck method are presented. The objective of this method is to extract a compact representation of a variable, considered the input, with minimal loss of mutual information with respect to another variable, considered the output. First, we introduce a split-and-merge algorithm based on the definition of an information channel between a set of regions (input) of the image and the intensity histogram bins (output). From this channel, the maximization of the mutual information gain is used to optimize the image partitioning. Then, the merging process of the regions obtained in the previous phase is carried out by minimizing the loss of mutual information. From the inversion of the above channel, we also present a new histogram clustering algorithm based on the minimization of the mutual information loss, where now the input variable represents the histogram bins and the output is given by the set of regions obtained from the above split-and-merge algorithm. Finally, we introduce two new clustering algorithms which show how the information bottleneck method can be applied to the registration channel obtained when two multimodal images are correctly aligned. Different experiments on 2-D and 3-D images show the behavior of the proposed algorithms

Fingerprint Segmentation

In this thesis, a new algorithm has been proposed to segment the foreground of the fingerprint from the image under consideration. The algorithm uses three features, mean, variance and coherence. Based on these features, a rule system is built to help the algorithm to efficiently segment the image. In addition, the proposed algorithm combine split and merge with modified Otsu. Both enhancements techniques such as Gaussian filter and histogram equalization are applied to enhance and improve the quality of the image. Finally, a post processing technique is implemented to counter the undesirable effect in the segmented image. Fingerprint recognition system is one of the oldest recognition systems in biometrics techniques. Everyone have a unique and unchangeable fingerprint. Based on this uniqueness and distinctness, fingerprint identification has been used in many applications for a long period. A fingerprint image is a pattern which consists of two regions, foreground and background. The foreground contains all important information needed in the automatic fingerprint recognition systems. However, the background is a noisy region that contributes to the extraction of false minutiae in the system. To avoid the extraction of false minutiae, there are many steps which should be followed such as preprocessing and enhancement. One of these steps is the transformation of the fingerprint image from gray-scale image to black and white image. This transformation is called segmentation or binarization. The aim for fingerprint segmentation is to separate the foreground from the background. Due to the nature of fingerprint image, the segmentation becomes an important and challenging task. The proposed algorithm is applied on FVC2000 database. Manual examinations from human experts show that the proposed algorithm provides an efficient segmentation results. These improved results are demonstrating in diverse experiments.

Time-resolved evolution of coherent structures in turbulent channels

El objetivo de esta tesis es estudiar la dinámica de la capa logarítmica de flujos turbulentos de pared. En concreto, proponemos un nuevo modelo estructural utilizando diferentes tipos de estructuras coherentes: sweeps, eyecciones, grupos de vorticidad y streaks. La herramienta utilizada es la simulación numérica directa de canales turbulentos. Desde los primeros trabajos de Theodorsen (1952), las estructuras coherentes han jugado un papel fundamental para entender la organización y dinámica de los flujos turbulentos. A día de hoy, datos procedentes de simulaciones numéricas directas obtenidas en instantes no contiguos permiten estudiar las propiedades fundamentales de las estructuras coherentes tridimensionales desde un punto de vista estadístico. Sin embargo, la dinámica no puede ser entendida en detalle utilizando sólo instantes aislados en el tiempo, sino que es necesario seguir de forma continua las estructuras. Aunque existen algunos estudios sobre la evolución temporal de las estructuras más pequeñas a números de Reynolds moderados, por ejemplo Robinson (1991), todavía no se ha realizado un estudio completo a altos números de Reynolds y para todas las escalas presentes de la capa logarítmica. El objetivo de esta tesis es llevar a cabo dicho análisis. Los problemas más interesantes los encontramos en la región logarítmica, donde residen las cascadas de vorticidad, energía y momento. Existen varios modelos que intentan explicar la organización de los flujos turbulentos en dicha región. Uno de los más extendidos fue propuesto por Adrian et al. (2000) a través de observaciones experimentales y considerando como elemento fundamental paquetes de vórtices con forma de horquilla que actúan de forma cooperativa para generar rampas de bajo momento. Un modelo alternativo fué ideado por del Álamo & Jiménez (2006) utilizando datos numéricos. Basado también en grupos de vorticidad, planteaba un escenario mucho más desorganizado y con estructuras sin forma de horquilla. Aunque los dos modelos son cinemáticamente similares, no lo son desde el punto de vista dinámico, en concreto en lo que se refiere a la importancia que juega la pared en la creación y vida de las estructuras. Otro punto importante aún sin resolver se refiere al modelo de cascada turbulenta propuesto por Kolmogorov (1941b), y su relación con estructuras coherentes medibles en el flujo. Para dar respuesta a las preguntas anteriores, hemos desarrollado un nuevo método que permite seguir estructuras coherentes en el tiempo y lo hemos aplicado a simulaciones numéricas de canales turbulentos con números de Reynolds lo suficientemente altos como para tener un rango de escalas no trivial y con dominios computacionales lo suficientemente grandes como para representar de forma correcta la dinámica de la capa logarítmica. Nuestros esfuerzos se han desarrollado en cuatro pasos. En primer lugar, hemos realizado una campaña de simulaciones numéricas directas a diferentes números de Reynolds y tamaños de cajas para evaluar el efecto del dominio computacional en las estadísticas de primer orden y el espectro. A partir de los resultados obtenidos, hemos concluido que simulaciones con cajas de longitud 2vr y ancho vr veces la semi-altura del canal son lo suficientemente grandes para reproducir correctamente las interacciones entre estructuras coherentes de la capa logarítmica y el resto de escalas. Estas simulaciones son utilizadas como punto de partida en los siguientes análisis. En segundo lugar, las estructuras coherentes correspondientes a regiones con esfuerzos de Reynolds tangenciales intensos (Qs) en un canal turbulento han sido estudiadas extendiendo a tres dimensiones el análisis de cuadrantes, con especial énfasis en la capa logarítmica y la región exterior. Las estructuras coherentes han sido identificadas como regiones contiguas del espacio donde los esfuerzos de Reynolds tangenciales son más intensos que un cierto nivel. Los resultados muestran que los Qs separados de la pared están orientados de forma isótropa y su contribución neta al esfuerzo de Reynolds medio es nula. La mayor contribución la realiza una familia de estructuras de mayor tamaño y autosemejantes cuya parte inferior está muy cerca de la pared (ligada a la pared), con una geometría compleja y dimensión fractal « 2. Estas estructuras tienen una forma similar a una ‘esponja de placas’, en comparación con los grupos de vorticidad que tienen forma de ‘esponja de cuerdas’. Aunque el número de objetos decae al alejarnos de la pared, la fracción de esfuerzos de Reynolds que contienen es independiente de su altura, y gran parte reside en unas pocas estructuras que se extienden más allá del centro del canal, como en las grandes estructuras propuestas por otros autores. Las estructuras dominantes en la capa logarítmica son parejas de sweeps y eyecciones uno al lado del otro y con grupos de vorticidad asociados que comparten las dimensiones y esfuerzos con los remolinos ligados a la pared propuestos por Townsend. En tercer lugar, hemos estudiado la evolución temporal de Qs y grupos de vorticidad usando las simulaciones numéricas directas presentadas anteriormente hasta números de Reynolds ReT = 4200 (Reynolds de fricción). Las estructuras fueron identificadas siguiendo el proceso descrito en el párrafo anterior y después seguidas en el tiempo. A través de la interseción geométrica de estructuras pertenecientes a instantes de tiempo contiguos, hemos creado gratos de conexiones temporales entre todos los objetos y, a partir de ahí, definido ramas primarias y secundarias, de tal forma que cada rama representa la evolución temporal de una estructura coherente. Una vez que las evoluciones están adecuadamente organizadas, proporcionan toda la información necesaria para caracterizar la historia de las estructuras desde su nacimiento hasta su muerte. Los resultados muestran que las estructuras nacen a todas las distancias de la pared, pero con mayor probabilidad cerca de ella, donde la cortadura es más intensa. La mayoría mantienen tamaños pequeños y no viven mucho tiempo, sin embargo, existe una familia de estructuras que crecen lo suficiente como para ligarse a la pared y extenderse a lo largo de la capa logarítmica convirtiéndose en las estructuras observas anteriormente y descritas por Townsend. Estas estructuras son geométricamente autosemejantes con tiempos de vida proporcionales a su tamaño. La mayoría alcanzan tamaños por encima de la escala de Corrsin, y por ello, su dinámica está controlada por la cortadura media. Los resultados también muestran que las eyecciones se alejan de la pared con velocidad media uT (velocidad de fricción) y su base se liga a la pared muy rápidamente al inicio de sus vidas. Por el contrario, los sweeps se mueven hacia la pared con velocidad -uT y se ligan a ella más tarde. En ambos casos, los objetos permanecen ligados a la pared durante 2/3 de sus vidas. En la dirección de la corriente, las estructuras se desplazan a velocidades cercanas a la convección media del flujo y son deformadas por la cortadura. Finalmente, hemos interpretado la cascada turbulenta, no sólo como una forma conceptual de organizar el flujo, sino como un proceso físico en el cual las estructuras coherentes se unen y se rompen. El volumen de una estructura cambia de forma suave, cuando no se une ni rompe, o lo hace de forma repentina en caso contrario. Los procesos de unión y rotura pueden entenderse como una cascada directa (roturas) o inversa (uniones), siguiendo el concepto de cascada de remolinos ideado por Richardson (1920) y Obukhov (1941). El análisis de los datos muestra que las estructuras con tamaños menores a 30η (unidades de Kolmogorov) nunca se unen ni rompen, es decir, no experimentan el proceso de cascada. Por el contrario, aquellas mayores a 100η siempre se rompen o unen al menos una vez en su vida. En estos casos, el volumen total ganado y perdido es una fracción importante del volumen medio de la estructura implicada, con una tendencia ligeramente mayor a romperse (cascada directa) que a unirse (cascade inversa). La mayor parte de interacciones entre ramas se debe a roturas o uniones de fragmentos muy pequeños en la escala de Kolmogorov con estructuras más grandes, aunque el efecto de fragmentos de mayor tamaño no es despreciable. También hemos encontrado que las roturas tienen a ocurrir al final de la vida de la estructura y las uniones al principio. Aunque los resultados para la cascada directa e inversa no son idénticos, son muy simétricos, lo que sugiere un alto grado de reversibilidad en el proceso de cascada. ABSTRACT The purpose of the present thesis is to study the dynamics of the logarithmic layer of wall-bounded turbulent flows. Specifically, to propose a new structural model based on four different coherent structures: sweeps, ejections, clusters of vortices and velocity streaks. The tool used is the direct numerical simulation of time-resolved turbulent channels. Since the first work by Theodorsen (1952), coherent structures have played an important role in the understanding of turbulence organization and its dynamics. Nowadays, data from individual snapshots of direct numerical simulations allow to study the threedimensional statistical properties of those objects, but their dynamics can only be fully understood by tracking them in time. Although the temporal evolution has already been studied for small structures at moderate Reynolds numbers, e.g., Robinson (1991), a temporal analysis of three-dimensional structures spanning from the smallest to the largest scales across the logarithmic layer has yet to be performed and is the goal of the present thesis. The most interesting problems lie in the logarithmic region, which is the seat of cascades of vorticity, energy, and momentum. Different models involving coherent structures have been proposed to represent the organization of wall-bounded turbulent flows in the logarithmic layer. One of the most extended ones was conceived by Adrian et al. (2000) and built on packets of hairpins that grow from the wall and work cooperatively to gen- ´ erate low-momentum ramps. A different view was presented by del Alamo & Jim´enez (2006), who extracted coherent vortical structures from DNSs and proposed a less organized scenario. Although the two models are kinematically fairly similar, they have important dynamical differences, mostly regarding the relevance of the wall. Another open question is whether such a model can be used to explain the cascade process proposed by Kolmogorov (1941b) in terms of coherent structures. The challenge would be to identify coherent structures undergoing a turbulent cascade that can be quantified. To gain a better insight into the previous questions, we have developed a novel method to track coherent structures in time, and used it to characterize the temporal evolutions of eddies in turbulent channels with Reynolds numbers high enough to include a non-trivial range of length scales, and computational domains sufficiently long and wide to reproduce correctly the dynamics of the logarithmic layer. Our efforts have followed four steps. First, we have conducted a campaign of direct numerical simulations of turbulent channels at different Reynolds numbers and box sizes, and assessed the effect of the computational domain in the one-point statistics and spectra. From the results, we have concluded that computational domains with streamwise and spanwise sizes 2vr and vr times the half-height of the channel, respectively, are large enough to accurately capture the dynamical interactions between structures in the logarithmic layer and the rest of the scales. These simulations are used in the subsequent chapters. Second, the three-dimensional structures of intense tangential Reynolds stress in plane turbulent channels (Qs) have been studied by extending the classical quadrant analysis to three dimensions, with emphasis on the logarithmic and outer layers. The eddies are identified as connected regions of intense tangential Reynolds stress. Qs are then classified according to their streamwise and wall-normal fluctuating velocities as inward interactions, outward interactions, sweeps and ejections. It is found that wall-detached Qs are isotropically oriented background stress fluctuations, common to most turbulent flows, and do not contribute to the mean stress. Most of the stress is carried by a selfsimilar family of larger wall-attached Qs, increasingly complex away from the wall, with fractal dimensions « 2. They have shapes similar to ‘sponges of flakes’, while vortex clusters resemble ‘sponges of strings’. Although their number decays away from the wall, the fraction of the stress that they carry is independent of their heights, and a substantial part resides in a few objects extending beyond the centerline, reminiscent of the very large scale motions of several authors. The predominant logarithmic-layer structures are sideby- side pairs of sweeps and ejections, with an associated vortex cluster, and dimensions and stresses similar to Townsend’s conjectured wall-attached eddies. Third, the temporal evolution of Qs and vortex clusters are studied using time-resolved DNS data up to ReT = 4200 (friction Reynolds number). The eddies are identified following the procedure presented above, and then tracked in time. From the geometric intersection of structures in consecutive fields, we have built temporal connection graphs of all the objects, and defined main and secondary branches in a way that each branch represents the temporal evolution of one coherent structure. Once these evolutions are properly organized, they provide the necessary information to characterize eddies from birth to death. The results show that the eddies are born at all distances from the wall, although with higher probability near it, where the shear is strongest. Most of them stay small and do not last for long times. However, there is a family of eddies that become large enough to attach to the wall while they reach into the logarithmic layer, and become the wall-attached structures previously observed in instantaneous flow fields. They are geometrically self-similar, with sizes and lifetimes proportional to their distance from the wall. Most of them achieve lengths well above the Corrsin’ scale, and hence, their dynamics are controlled by the mean shear. Eddies associated with ejections move away from the wall with an average velocity uT (friction velocity), and their base attaches very fast at the beginning of their lives. Conversely, sweeps move towards the wall at -uT, and attach later. In both cases, they remain attached for 2/3 of their lives. In the streamwise direction, eddies are advected and deformed by the local mean velocity. Finally, we interpret the turbulent cascade not only as a way to conceptualize the flow, but as an actual physical process in which coherent structures merge and split. The volume of an eddy can change either smoothly, when they are not merging or splitting, or through sudden changes. The processes of merging and splitting can be thought of as a direct (when splitting) or an inverse (when merging) cascade, following the ideas envisioned by Richardson (1920) and Obukhov (1941). It is observed that there is a minimum length of 30η (Kolmogorov units) above which mergers and splits begin to be important. Moreover, all eddies above 100η split and merge at least once in their lives. In those cases, the total volume gained and lost is a substantial fraction of the average volume of the structure involved, with slightly more splits (direct cascade) than mergers. Most branch interactions are found to be the shedding or absorption of Kolmogorov-scale fragments by larger structures, but more balanced splits or mergers spanning a wide range of scales are also found to be important. The results show that splits are more probable at the end of the life of the eddy, while mergers take place at the beginning of the life. Although the results for the direct and the inverse cascades are not identical, they are found to be very symmetric, which suggests a high degree of reversibility of the cascade process.