477 research outputs found
Effects of Water Stress on Seed Production in Ruzi Grass \u3ci\u3e(Brachiaria ruziziensis Germain and Everard)\u3c/i\u3e
Water stress at different stages of reproductive development influenced seed yield in Ruzi grass differently. Under mild water stress, the earlier in the reproductive developmental stage the stress was applied (before ear emergence) the faster the plants recovered and the less the ultimate damage to inflorescence structure and seed set compared with the situation where water stress occurred during the later stages after inflorescences had emerged. Conversely, severe water stress before ear emergence had a severe effect in damaging both inflorescence numbers and seed quality. Permanent damage to the reproductive structures resulted in deformed inflorescences. Moreover, basal vegetative tillers were stunted and were capable of only limited regrowth after re-watering
The Little-Hopfield model on a Random Graph
We study the Hopfield model on a random graph in scaling regimes where the
average number of connections per neuron is a finite number and where the spin
dynamics is governed by a synchronous execution of the microscopic update rule
(Little-Hopfield model).We solve this model within replica symmetry and by
using bifurcation analysis we prove that the spin-glass/paramagnetic and the
retrieval/paramagnetictransition lines of our phase diagram are identical to
those of sequential dynamics.The first-order retrieval/spin-glass transition
line follows by direct evaluation of our observables using population dynamics.
Within the accuracy of numerical precision and for sufficiently small values of
the connectivity parameter we find that this line coincides with the
corresponding sequential one. Comparison with simulation experiments shows
excellent agreement.Comment: 14 pages, 4 figure
Phase transitions in optimal unsupervised learning
We determine the optimal performance of learning the orientation of the
symmetry axis of a set of P = alpha N points that are uniformly distributed in
all the directions but one on the N-dimensional sphere. The components along
the symmetry breaking direction, of unitary vector B, are sampled from a
mixture of two gaussians of variable separation and width. The typical optimal
performance is measured through the overlap Ropt=B.J* where J* is the optimal
guess of the symmetry breaking direction. Within this general scenario, the
learning curves Ropt(alpha) may present first order transitions if the clusters
are narrow enough. Close to these transitions, high performance states can be
obtained through the minimization of the corresponding optimal potential,
although these solutions are metastable, and therefore not learnable, within
the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper
contains one new section, Bayesian versus optimal solutions, where we explain
in detail the results supporting our claim that bayesian learning may not be
optimal. Figures 4 of the first submission was difficult to understand. We
replaced it by two new figures (Figs. 4 and 5 in this new version) containing
more detail
Double-Blind Controlled Assessment of the Effect of Intra-Articular Hydrocortisone and Urokinase in Rheumatoid Arthritis
The merits of intra-articular urokinase in the treatment of rheumatoid arthritis are discussed. The results of a double-blind controlled study of its use in the knee joints following intra-articular hydrocortisone are presented
A Hebbian approach to complex network generation
Through a redefinition of patterns in an Hopfield-like model, we introduce
and develop an approach to model discrete systems made up of many, interacting
components with inner degrees of freedom. Our approach clarifies the intrinsic
connection between the kind of interactions among components and the emergent
topology describing the system itself; also, it allows to effectively address
the statistical mechanics on the resulting networks. Indeed, a wide class of
analytically treatable, weighted random graphs with a tunable level of
correlation can be recovered and controlled. We especially focus on the case of
imitative couplings among components endowed with similar patterns (i.e.
attributes), which, as we show, naturally and without any a-priori assumption,
gives rise to small-world effects. We also solve the thermodynamics (at a
replica symmetric level) by extending the double stochastic stability
technique: free energy, self consistency relations and fluctuation analysis for
a picture of criticality are obtained
Statistical Mechanics of Soft Margin Classifiers
We study the typical learning properties of the recently introduced Soft
Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the
tools of Statistical Mechanics. We derive analytically the behaviour of the
learning curves in the regime of very large training sets. We obtain
exponential and power laws for the decay of the generalization error towards
the asymptotic value, depending on the task and on general characteristics of
the distribution of stabilities of the patterns to be learned. The optimal
learning curves of the SMCs, which give the minimal generalization error, are
obtained by tuning the coefficient controlling the trade-off between the error
and the regularization terms in the cost function. If the task is realizable by
the SMC, the optimal performance is better than that of a hard margin Support
Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review
Finite Connectivity Attractor Neural Networks
We study a family of diluted attractor neural networks with a finite average
number of (symmetric) connections per neuron. As in finite connectivity spin
glasses, their equilibrium properties are described by order parameter
functions, for which we derive an integral equation in replica symmetric (RS)
approximation. A bifurcation analysis of this equation reveals the locations of
the paramagnetic to recall and paramagnetic to spin-glass transition lines in
the phase diagram. The line separating the retrieval phase from the spin-glass
phase is calculated at zero temperature. All phase transitions are found to be
continuous.Comment: 17 pages, 4 figure
Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices
We calculate equilibrium solutions for Ising spin models on `small world'
lattices, which are constructed by super-imposing random and sparse Poissonian
graphs with finite average connectivity c onto a one-dimensional ring. The
nearest neighbour bonds along the ring are ferromagnetic, whereas those
corresponding to the Poisonnian graph are allowed to be random. Our models thus
generally contain quenched connectivity and bond disorder. Within the replica
formalism, calculating the disorder-averaged free energy requires the
diagonalization of replicated transfer matrices. In addition to developing the
general replica symmetric theory, we derive phase diagrams and calculate
effective field distributions for two specific cases: that of uniform sparse
long-range bonds (i.e. `small world' magnets), and that of (+J/-J) random
sparse long-range bonds (i.e. `small world' spin-glasses).Comment: 22 pages, LaTeX, IOP macros, eps figure
Retarded Learning: Rigorous Results from Statistical Mechanics
We study learning of probability distributions characterized by an unknown
symmetry direction. Based on an entropic performance measure and the
variational method of statistical mechanics we develop exact upper and lower
bounds on the scaled critical number of examples below which learning of the
direction is impossible. The asymptotic tightness of the bounds suggests an
asymptotically optimal method for learning nonsmooth distributions.Comment: 8 pages, 1 figur
The signal-to-noise analysis of the Little-Hopfield model revisited
Using the generating functional analysis an exact recursion relation is
derived for the time evolution of the effective local field of the fully
connected Little-Hopfield model. It is shown that, by leaving out the feedback
correlations arising from earlier times in this effective dynamics, one
precisely finds the recursion relations usually employed in the signal-to-noise
approach. The consequences of this approximation as well as the physics behind
it are discussed. In particular, it is pointed out why it is hard to notice the
effects, especially for model parameters corresponding to retrieval. Numerical
simulations confirm these findings. The signal-to-noise analysis is then
extended to include all correlations, making it a full theory for dynamics at
the level of the generating functional analysis. The results are applied to the
frequently employed extremely diluted (a)symmetric architectures and to
sequence processing networks.Comment: 26 pages, 3 figure
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