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The hidden Markov tree models were introduced by Crouse, Nowak and Baraniuk in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their article, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and termed it the " upward-downward algorithm ". This algorithm is subject to the same(More)
The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex network of over 50 potentially interacting(More)
The knowledge of the state sequences that explain a given observed sequence for a known hidden Markovian model is the basis of various methods that may be divided into three categories: (i) enumeration of state sequences; (ii) summary of the possible state sequences in state profiles; (iii) computation of a global measure of the state sequence uncertainty.(More)
This study aims to explore and model the changes in growth unit (GU) branching patterns during tree ontogeny. The question was addressed in apple trees cv. "Fuji", by analysing the relative impact of GU length and within-tree position. The development of two 6-year-old trees was recorded over 6 years. The fate of axillary buds along each GU was represented(More)
Observed growth, as given, for instance, by the length of successive annual shoots along the main axis of a plant, is mainly the result of two components: an ontogenetic component and an environmental component. An open question is whether the ontogenetic component along an axis at the growth unit or annual shoot scale takes the form of a trend or of a(More)
This paper addresses the identification and characterization of developmental patterns in the whole structure of a sympodial species, the apple tree. Dedicated stochastic models (hidden variable-order Markov chains) were used to (i) categorise growth units (GUs) on the basis of their morphological characteristics (number of nodes and presence/absence of(More)
Root architecture is a crucial part of plant adaptation to soil heterogeneity and is mainly controlled by root branching. The process of root system development can be divided into two successive steps: lateral root initiation and lateral root development/emergence which are controlled by different fluxes of the plant hormone auxin. While shoot architecture(More)