638,899 research outputs found
Local dimension and finite time prediction in spatiotemporal chaotic systems
We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett.
81 5878 (2001)] provides a direct relationship between dimension and
predictability in spatiotemporal chaotic systems. Regions of low dimension are
identified as having high predictability and vice-versa. This conclusion is
reached by using methods from dynamical systems theory and Bayesian modelling.
We emphasize in this work the consequences for short time forecasting and
examine the relevance for factor analysis. Although we concentrate on coupled
map lattices and coupled nonlinear oscillators for convenience, any other
spatially distributed system could be used instead, such as turbulent fluid
flows.Comment: 5 pagers, 7 EPS figure
Natural Suppression of Higgsino-Mediated Proton Decay in Supersymmetric SO(10)
In supersymmetric Grand Unified Theories, proton decay mediated by the
color--triplet higgsino is generally problematic and requires some fine--tuning
of parameters. We present a mechanism which naturally suppresses such dimension
5 operators in the context of SUSY . The mechanism, which implements
natural doublet--triplet splitting using the adjoint higgs, converts these
dimension 5 operators effectively into dimension 6. By explicitly computing the
higgs spectrum and the resulting threshold uncertainties we show that the
successful prediction of is maintained {\it as a prediction}
in this scheme. It is argued that only a weak suppression of the higgsino
mediated proton decay is achievable within SUSY without fine--tuning,
in contrast to a strong suppression in SUSY .Comment: 39 pages (3 Feynman graphs not included), in Plain LaTeX, BA-93-2
Optimal Categorization
The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and it is generally acknowledged that one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object's value in the other dimension. The subject partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension. The average value in the second dimension, of objects in this category in the data base, is used as prediction for the object at hand. At the end of each period the second dimension is observed and the observation is stored in the data base. The main result is that the optimal number of categories is determined by a trade-off between (a) decreasing the size of categories in order to enhance category homogeneity, and (b) increasing the size of categories in order to enhance category sample size.Categorization; Priors; Prediction; Similarity-Based Reasoning.
Gravitational uncertainties from dimension-six operators on supersymmetric GUT predictions
We consider the gravity induced dimension six terms in addition to the
dimension five terms in the SUSY GUT Lagrangian and find that the prediction
for may be washed out completely in supersymmetric grand unified
theories unless the triplet higgs mass is smaller than GeV.Comment: 7 pages,latex.Title of original version changed,text added and a
figure has been added.Figure is available on request.To appear as a brief
Report in Phys.Rev.
The 16th moment of the three loop anomalous dimension of the non-singlet transversity operator in QCD
We present the result of the three loop anomalous dimension of non-singlet
transversity operator in QCD for the Mellin moment N=16. The obtained result
coincides with the prediction from arXiv:1203.1022 and can serve as a
confirmation of the correctness of the general expression for three loop
anomalous dimension of non-singlet transversity operator in QCD for the
arbitrary Mellin moment.Comment: 7 pages, 1 figure, minor changes in the tex
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