Symmetric Maximum Research Articles

On the minimum rank of not necessarily symmetric matrices: A preliminary study

The minimum rank of a directed graph Γ is defined to be the smallest possible rank over all real matrices whose ijth entry is nonzero whenever (i,j) is an arc in Γ and is zero otherwise. The symmetric minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i ≠ j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. Maximum nullity is equal to the difference between the order of the graph and minimum rank in either case. Definitions of various graph parameters used to bound symmetric maximum nullity, including path cover number and zero forcing number, are extended to digraphs, and additional parameters related to minimum rank are introduced. It is shown that for directed trees, maximum nullity, path cover number, and zero forcing number are equal, providing a method to compute minimum rank for directed trees. It is shown that the minimum rank problem for any given digraph or zero-nonzero pattern may be converted into a symmetric minimum rank problem.

A representation of a comonotone- [formula omitted]-additive and monotone functional by two Sugeno integrals

There is obtained a representation of a comonotone- ◯ ∨ -additive, weak ◯ ∧ -homogeneous and monotone functional L (defined on the class of functions on finite set) as a symmetric maximum of two Sugeno integrals. This representation is a generalization of certain previous results, which are useful for cumulative prospect theory. As a consequence of a result on general fuzzy rank and sign-dependent functionals considered on functions defined on the infinitely countable basic set X it is obtained that the symmetric Sugeno integral is comonotone- ◯ ∨ -additive functional on the class of functions with finite support.

Comparison of criteria on the direction of crack extension

There are three famous criteria for the prediction on the direction of crack extension: maximum energy release rate criterion, local symmetric criterion and maximum stress criterion. It has already been proved that these criteria are different. In this paper, we show how to measure the difference between maximum energy release rate criterion and maximum stress criterion. The results in this paper and special solutions in Amestoy and Leblond (Internat. J. Solids Struct. 29 (1992) 465) indicate that it is enough to use the maximum stress criterion for the numerical prediction of crack path, if the stress intensity factor of the shearing mode is not too big.

Symmetric adaptive maximum likelihood estimationfor noise cancellation and signal separation

The symmetric adaptive maximum likelihood estimation (SAMLE) algorithm is proposed. It is shown to be a generalisation of the symmetric adaptive decorrelation (SAD) algorithm for noise cancellation and signal separation. Both the SAD and SAMLE algorithms are applied to the separation of a mixture of natural speech recorded in a realistic acoustic environment. A comparative simulation confirms that the SAMLE algorithm provides superior separation capabilities.

Nonuniform Dust Outflow Observed around Infrared Object NML Cygni

Measurements by the U.C. Berkeley Infrared Spatial Interferometer at 11.15 micron have yielded strong evidence for multiple dust shells and/or significant asymmetric dust emission around NML Cyg. New observations reported also include multiple 8-13 micron spectra taken from 1994-1995 and N band (10.2 micron) photometry from 1980-1992. These and past measurements are analyzed and fitted to a model of the dust distribution around NML Cyg. No spherically symmetric single dust shell model is found consistent with both near- and mid-infrared observations. However, a circularly symmetric maximum entropy reconstruction of the 11 micron brightness distribution suggests a double shell model for the dust distribution. Such a model, consisting of a geometrically thin shell of intermediate optical depth ($\tau_{11 micron} \sim 1.9$) plus an outer shell ($\tau_{11 micron} \sim 0.33$), is consistent not only with the 11 micron visibility data, but also with near-infrared speckle measurements, the broadband spectrum, and the 9.7 micron silicate feature. The outer shell, or large scale structure, is revealed only by long-baseline interferometry at 11 micron, being too cold ($\sim$ 400 K) to contribute in the near-infrared and having no unambiguous spectral signature in the mid-infrared. The optical constants of Ossenkopf, Henning, & Mathis (1992) proved superior to the Draine & Lee (1984) constants in fitting the detailed shape of the silicate feature and broadband spectrum for this object. Recent observations of H$_2$O maser emission around NML Cyg by Richards, Yates, & Cohen (1996) are consistent with the location of the two dust shells and provide further evidence for the two-shell model.

Moments of the maximum entropy and the symmetric maximum entropy distribution

Abstract Simulation results are described for four estimators of moments of a normal distribution: the sample and maximum entropy (ME) moments and those obtained when the sample or ME distribution is symmetrized. The discussion includes the small-sample bias and the gain in efficiency which results from the knowledge that the parent distribution is continuous and/or symmetric.

The symmetric maximum entropy distribution

The symmetric maximum entropy (ME) distribution is introduced based on symmetrized order statistics. Its properties (including higher-order moments) are compared with those of the non-symmetric ME distribution.

Critical order-parameter relaxation and hypersonic attenuation in helium

The asymmetry of the temperature dependence, the broad symmetric maximum, and the frequency dependence of hypersonic attenuation in helium near the λ-point can be understood qualitatively in terms of the critical relaxation of fluctuations in the order parameter.