751 research outputs found

### Towards understanding tree root profiles: simulating hydrologically optimal strategies for root distribution

In this modelling study differences in vertical root distributions measured in four contrasting forest locations in the Netherlands were investigated. Root distributions are seen as a reflection of the plant’s optimisation strategy, based on hydrological grounds. The 'optimal' root distribution is defined as the one that maximises the water uptake from the root zone over a period of ten years. The optimal root distributions of four forest locations with completely different soil physical characteristics are calculated using the soil hydrological model SWIF. Two different model configurations for root interactions were tested: the standard model configuration in which one single root profile was used (SWIF-NC), and a model configuration in which two root profiles compete for the same available water (SWIF-C). The root profiles were parameterised with genetic algorithms. The fitness of a certain root profile was defined as the amount of water uptake over a simulation period of ten years. The root profiles of SWIF-C were optimised using an evolutionary game. The results showed clear differences in optimal root distributions between the various sites and also between the two model configurations. Optimisation with SWIF-C resulted in root profiles that were easier to interpret in terms of feasible biological strategies. Preferential water uptake in wetter soil regions was an important factor for interpretation of the simulated root distributions. As the optimised root profiles still showed differences with measured profiles, this analysis is presented, not as the final solution for explaining differences in root profiles of vegetation but as a first step using an optimisation theory to increase understanding of the root profiles of trees.</p> <p style='line-height: 20px;'><b>Keywords:</b> forest hydrology, optimisation, root

### Towards understanding tree root profiles: simulating hydrologically optimal strategies for root distribution

International audienceIn this modelling study differences in vertical root distributions measured in four contrasting forest locations in the Netherlands were investigated. Root distributions are seen as a reflection of the plant's optimisation strategy, based on hydrological grounds. The "optimal" root distribution is defined as the one that maximises the water uptake from the root zone over a period of ten years. The optimal root distributions of four forest locations with completely different soil physical characteristics are calculated using the soil hydrological model SWIF. Two different model configurations for root interactions were tested: the standard model configuration in which one single root profile was used (SWIF-NC), and a model configuration in which two root profiles compete for the same available water (SWIF-C). The root profiles were parameterised with genetic algorithms. The fitness of a certain root profile was defined as the amount of water uptake over a simulation period of ten years. The root profiles of SWIF-C were optimised using an evolutionary game. The results showed clear differences in optimal root distributions between the various sites and also between the two model configurations. Optimisation with SWIF-C resulted in root profiles that were easier to interpret in terms of feasible biological strategies. Preferential water uptake in wetter soil regions was an important factor for interpretation of the simulated root distributions. As the optimised root profiles still showed differences with measured profiles, this analysis is presented, not as the final solution for explaining differences in root profiles of vegetation but as a first step using an optimisation theory to increase understanding of the root profiles of trees. Keywords: forest hydrology, optimisation, root

### Storage capacity of correlated perceptrons

We consider an ensemble of $K$ single-layer perceptrons exposed to random
inputs and investigate the conditions under which the couplings of these
perceptrons can be chosen such that prescribed correlations between the outputs
occur. A general formalism is introduced using a multi-perceptron costfunction
that allows to determine the maximal number of random inputs as a function of
the desired values of the correlations. Replica-symmetric results for $K=2$ and
$K=3$ are compared with properties of two-layer networks of tree-structure and
fixed Boolean function between hidden units and output. The results show which
correlations in the hidden layer of multi-layer neural networks are crucial for
the value of the storage capacity.Comment: 16 pages, Latex2

### Weak measurement and rapid state reduction in bipartite quantum systems

In this paper we consider feedback control algorithms for the rapid
purification of a bipartite state consisting of two qubits, when the observer
has access to only one of the qubits. We show 1) that the algorithm that
maximizes the average purification rate is not the same as that that for a
single qubit, and 2) that it is always possible to construct an algorithm that
generates a deterministic rate of purification for {\em both} qubits. We also
reveal a key difference between projective and continuous measurements with
regard to state-purification.Comment: 4 pages, 3 figure

### A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such
as those consisting of small numbers of atoms and photons--is a delicate
business. The fundamental uncertainty that is inherently present at this scale
manifests itself in the unavoidable presence of noise, making this a novel
field of application for stochastic estimation and control theory. In this
expository paper we demonstrate estimation and feedback control of quantum
mechanical systems in what is essentially a noncommutative version of the
binomial model that is popular in mathematical finance. The model is extremely
rich and allows a full development of the theory, while remaining completely
within the setting of finite-dimensional Hilbert spaces (thus avoiding the
technical complications of the continuous theory). We introduce discretized
models of an atom in interaction with the electromagnetic field, obtain
filtering equations for photon counting and homodyne detection, and solve a
stochastic control problem using dynamic programming and Lyapunov function
methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be
found at http://minty.caltech.edu/papers.ph

### Training a perceptron in a discrete weight space

On-line and batch learning of a perceptron in a discrete weight space, where
each weight can take $2 L+1$ different values, are examined analytically and
numerically. The learning algorithm is based on the training of the continuous
perceptron and prediction following the clipped weights. The learning is
described by a new set of order parameters, composed of the overlaps between
the teacher and the continuous/clipped students. Different scenarios are
examined among them on-line learning with discrete/continuous transfer
functions and off-line Hebb learning. The generalization error of the clipped
weights decays asymptotically as $exp(-K \alpha^2)$/$exp(-e^{|\lambda|
\alpha})$ in the case of on-line learning with binary/continuous activation
functions, respectively, where $\alpha$ is the number of examples divided by N,
the size of the input vector and $K$ is a positive constant that decays
linearly with 1/L. For finite $N$ and $L$, a perfect agreement between the
discrete student and the teacher is obtained for $\alpha \propto \sqrt{L
\ln(NL)}$. A crossover to the generalization error $\propto 1/\alpha$,
characterized continuous weights with binary output, is obtained for synaptic
depth $L > O(\sqrt{N})$.Comment: 10 pages, 5 figs., submitted to PR

- …