Sign Symmetry Research Articles

Direct evidence for the trigonal symmetry of shallow phosphorus acceptors in ZnSe

Spin-flip Raman scattering has been used to provide direct experimental evidence that shallow phosphorus acceptors in relaxed ZnSe epitaxial layers grown on GaAs lie at sites of predominantly trigonal local symmetry. As a consequence, the energy of the heavy-hole bound exciton is about 0.45 meV less than that of the light exciton. This splitting is significantly smaller than (and of opposite sign and different symmetry to) the valence-band splitting of 3 meV observed due to the macroscopic biaxial tensile strain in the same specimens. The behavior is in complete contrast to that of nitrogen acceptors, for which no trigonal field is observed. The experiments provide confirmation of the behavior predicted by previous pseudopotential total-energy calculations for the shallow acceptor states formed by these two different group-V dopants when substituting at selenium sites.

Graph theoretic methods for matrix completion problems

A pattern is a list of positions in an n×n real matrix. A matrix completion problem for the class of Π-matrices asks whether every partial Π-matrix whose specified entries are exactly the positions of the pattern can be completed to a Π-matrix. We survey the current state of research on Π-matrix completion problems for many subclasses Π of P 0 -matrices, including positive definite matrices, M-matrices, inverse M-matrices, P-matrices, and matrices defined by various sign symmetry and positivity conditions on P 0 - and P-matrices. Graph theoretic techniques used to study completion problems are discussed. Several new results are also presented, including the solution to the M 0 -matrix completion problem and the sign symmetric P 0 -matrix completion problem.

Ising-Type and Other Transitions in One-Dimensional Coupled Map Lattices with Sign Symmetry

We consider a one-dimensional lattice of expanding antisymmetric maps [−1, 1]→[−1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter e is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as e grows beyond some critical value ec. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as e approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.

Percolation in sign-symmetric random fields: Topological aspects and numerical modeling

The topology of percolation in random scalar fields psi(x) with sign symmetry [i.e., that the statistical properties of the functions psi(x) and -psi(x) are identical] is analyzed. Based on methods of general topology, we show that the zero set psi(x)=0 of the n-dimensional (n>/=2) sign-symmetric random field psi(x) contains a (connected) percolating subset under the condition |nablapsi(x)| not equal0 everywhere except in domains of negligible measure. The fractal geometry of percolation is analyzed in more detail in the particular case of the two-dimensional (n=2) fields psi(x). The improved Alexander-Orbach conjecture [Phys. Rev. E 56, 2437 (1997)] is applied analytically to obtain estimates of the main fractal characteristics of the percolating fractal sets generated by the horizontal "cuts," psi(x)=h, of the field psi(x). These characteristics are the Hausdorff fractal dimension of the set, D, and the index of connectivity, straight theta. We advocate an unconventional approach to studying the geometric properties of fractals, which involves methods of homotopic topology. It is shown that the index of connectivity, straight theta, of a fractal set is the topological invariant of this set, i.e., it remains unchanged under the homeomorphic deformations of the fractal. This issue is explicitly used in our study to find the Hausdorff fractal dimension of the single isolevels of the field psi(x), as well as the related geometric quantities. The results obtained are analyzed numerically in the particular case when the random field psi(x) is given by a fractional Brownian surface whose topological properties recover well the main assumptions of our consideration.

Effect of self-phase modulation in chirped-pulse-amplification-like schemes

A detailed analytical investigation is made of the effect of nonlinear self-phase modulation in chirped-pulse-amplification-like schemes. It is demonstrated that self-phase modulation in the amplifier between the stretcher and the compressor breaks the dispersive sign symmetry of the configuration. This implies that, although self-phase modulation is usually considered a deleterious effect, different situations are possible, depending on the parameter regimes considered. In particular, the influence of self-phase modulation on the low-intensity wings of the compressed pulse may be more or less deleterious, depending on the dispersive sign combination of the stretcher and the compressor; in certain parameter regimes, it may in fact even enhance the pulse compression.

Not all GKK τ-matrices are stable

Hermitian positive definite, totally positive, and nonsingular M -matrices enjoy many common properties, in particular: (A) positivity of all principal minors, (B) weak sign symmetry, (C) eigenvalue monolonicity, (D) positive stability. The class of GKK matrices is defined by properties (A) and (B), whereas the class of nonsingular τ-matrices by (A) and (C). It was conjectured that: (A), (B) ⇒ (D) [D. Carlson, J. Res. Nat. Bur. Standards Sect. B 78 (1974) 1–2], (A), (C) ⇒ (D) [G.M. Engel and H. Schneider, Linear and Multilinear Algebra 4 (1976) 155–176]. (A), (B) ⇒ a property stronger than (D) [R. Varga, Numerical Methods in Linear Algebra, 1978, pp. 5–15], (A), (B), (C) ⇒ (D) [D. Hershkowitz, Linear Algebra Appl. 171 (1992) 161–186]. We describe a class of unstable GKK τ-matrices, thus disproving all four conjectures.

Symmetry of a liquid and symmetry breaking at the glass transition

For the first time a liquid is considered from the point of view of Shubnikov antisymmetry (black-white or sign symmetry), a method that permits one to find a hidden symmetry of the liquid whose breaking reveals itself directly at the glass transition. This approach gives the opportunity to consider symmetries of different types of elementary motions in liquids, the symmetry-stipulated properties of liquids, the nature of the symmetry of the order parameter for the glass transition and, as a whole, the dynamical structure of the liquid on the scales of short-, medium-, and long-range order.

Symmetry of neurological signs in Pakistani patients with probable inherited spastic cerebral palsy.

Seven Pakistani families are described with children manifesting a spastic cerebral palsy-like syndrome. One feature common to all affected patients was symmetry of neurological signs. Only one of these families had been offered genetic counselling and fewer than half had undergone clinical investigations. The importance of symmetry of neurological signs is reaffirmed as an indicator of a probable genetic aetiology in children with spasticity. Many families at risk of recurrence are not offered appropriate genetic advice, and some children with potentially diagnosable conditions are given a label of cerebral palsy without investigation of possible underlying inherited disorders.

Multiple system atrophy presenting as parkinsonism: clinical features and diagnostic criteria.

To evaluate the possibility that parkinsonian signs may be the only presenting feature of multiple system atrophy (MSA), parkinsonian patients were studied who had no atypical clinical signs and had no symptoms of autonomic dysfunction, but who reported that they had not experienced the anticipated good response to dopaminergic treatment. These stringent criteria identified 20 patients from a series of 298 consecutive parkinsonian outpatients. The following clinical pointers were analysed: (a) rate of disease progression; (b) symmetry of parkinsonian symptoms and signs; (c) occurrence of resting tremor during the first three years from onset. In addition, all patients underwent (d) acute and chronic challenge with dopaminergic drugs; (e) cardiovascular reflex autonomic function tests; (f) high field MRI. Rapid progression of disease was seen in 45% of patients, onset was symmetric in 25%, tremor was absent at onset in 70%, response to dopaminergic drug challenges was inadequate in 40%, abnormal cardiovascular reflexes occurred in 50%, and some abnormal MRI finding occurred in 35% of cases. Each of these features was equally weighted by giving to each patient a 0 to 6 point score corresponding to the number of abnormal findings. Fifteen patients scoring higher than 1 were considered at risk for having MSA: five of them were classified as clinically possible (score 2), six as clinically probable (score 3-4), and four patients were classified as clinically definite multiple system atrophy (score 5). The six pointers considered were variably combined in each patient, none of them being universally abnormal in patients with high scores. The patients were followed up for a mean 2.1 (SEM 0.65) years. All but one of the 10 patients prospectively classified as probable or definite MSA developed unequivocal clinical signs of fully symptomatic MSA. A receiver operator characteristic cure was plotted for the prospective score based on follow up diagnosis. The best compromise for trade off between sensitivity and specificity was a cut off value at a score of 3. The sensitivity and specificity of the individual pointers considered to predict fully symptomatic MSA varied considerably, and no single item could predict whether patients presenting with just parkinsonian signs went on during the two year follow up period to develop fully symptomatic MSA. Instead, the number of abnormalities offered a predictive value for the clinical prognosis of these parkinsonian patients.

Phonological Deletion Revisited: Errors in Young Children’s Two-Handed Signs

The omission or deletion of one hand from two-handed signs was examined in 9 young children of deaf parents. The patterns of hand deletion found in the early signs of these children were quite similar to those reported by Battison (1974) for adult signers. Battison accounted for the deletion patterns he observed largely by sign symmetry. Analyses of the present children’s deletions, however, revealed that the likelihood of hand deletion was also highly related to the type of contact the sign required. Deletion was most frequent in signs that involved contact with the signer’s body. This finding is interpreted as indicating that the likelihood of hand deletion in ASL is related to the amount of information about the location aspect of the sign that would be lost when the sign is produced with only one hand. Evidence for the phonological process of assimilation in the children’s early signs and the children’s accuracy for handshapes in two-handed (as compared with one-handed) signs also is examined.

Matrices with Sign Symmetric Diagonal Shifts or Scalar Shifts

We generalize the concepts of sign symmetry and weak sign symmetry by defining k-sign symmetric matrices. For a positive integer k, we show that all diagonal shifts of an irreducible matrix are k-sign symmetric if and only if the matrix is diagonally similar to a Hermitian matrix. A similar result holds for scalar shifts, but requires an additional condition in the case $k = 1$. Extensions are given to reducible matrices.

Class G, and a unification problem

In 1958, Karl Goldberg proved the following: Theorem G . Suppose A =( a ij ) is an n × n matrix over the complex field, with the following properties: (1) a ij a ji ⩾0 for i , j =1,2,…, n , and (2) a i 1 i 2 a i 2 i 3 ⋯ a i s i i = a i 2 i 1 a i 3 i 2 ⋯ a i 1 i s for all s =1,2,…, n and i t =1,2,…, n . Then A has only real characteristic values. Definition . Let G n denote the class of n × n matrices over C , the complex field, which satisfy the Goldberg conditions (1) and (2). We investigate some properties of class G related to the following topics: Schur complements, weak sign symmetry, and inequalities due to Oppenheim for positive definite matrices, and an analogue due to Markham for tridiagonal, oscillatory matrices.