230 research outputs found
Bulk behaviour of Schur-Hadamard products of symmetric random matrices
We develop a general method for establishing the existence of the Limiting
Spectral Distributions (LSD) of Schur-Hadamard products of independent
symmetric patterned random matrices. We apply this method to show that the LSDs
of Schur-Hadamard products of some common patterned matrices exist and identify
the limits. In particular, the Schur-Hadamard product of independent Toeplitz
and Hankel matrices has the semi-circular LSD. We also prove an invariance
theorem that may be used to find the LSD in many examples.Comment: 27 pages, 1 figure; to appear, Random Matrices: Theory and
Applications. This is the final version, incorporating referee comment
Bulk behaviour of skew-symmetric patterned random matrices
Limiting Spectral Distributions (LSD) of real symmetric patterned matrices
have been well-studied. In this article, we consider
skew-symmetric/anti-symmetric patterned random matrices and establish the LSDs
of several common matrices. For the skew-symmetric Wigner, skew-symmetric
Toeplitz and the skew-symmetric Circulant, the LSDs (on the imaginary axis) are
the same as those in the symmetric cases. For the skew-symmetric Hankel and the
skew-symmetric Reverse Circulant however, we obtain new LSDs. We also show the
existence of the LSDs for the triangular versions of these matrices.
We then introduce a related modification of the symmetric matrices by
changing the sign of the lower triangle part of the matrices. In this case, the
modified Wigner, modified Hankel and the modified Reverse Circulants have the
same LSDs as their usual symmetric counterparts while new LSDs are obtained for
the modified Toeplitz and the modified Symmetric Circulant.Comment: 21 pages, 2 figure
Data broadcasting and reduction, prefix computation, and sorting on reduced hypercube (RH) parallel computers
The binary hypercube parallel computer has been very popular due to its rich interconnection structure and small average internode distance which allow the efficient embedding of frequently used topologies. Communication patterns of many parallel algorithms also match the hypercube topology. The hypercube has high VLSI complexity. however. due to the logarithmic increase in the number of connections to each node with the increase in the number of dimensions of the hypercube. The reduced hypercube (RH) interconnection network. which is obtained by a uniform reduction in the number of links for each hypercube node. yields lower-complexity interconnection networks when compared to hypercubes with the same number of nodes. It has been shown elsewhere that the RH interconnection network achieves performance comparable to that of the hypercube. at lower hardware cost. The reduced VLSI complexity of the RH also permits the construction of larger systems. thus. making the RH suitable for massively parallel processing. This thesis proposes algorithms for data broadcasting and reduction. prefix computation, and sorting on the RH parallel computer. All these operations are fundamental to many parallel algorithms. A worst case analysis of each algorithm is given and compared with equivalent- algorithms for the regular hypercube. It is shown that the proposed algorithms for the RH yield performance comparable to that for the regular hypercube
Promoting Higher Order Thinking In MIS/ CIS Students Using Class Exercises
It has been argued by many writers that it is necessary to develop critical thinking skills in MIS/CIS students because these skills are needed by them to tackle the complexities of real life problems that they are likely to face. While the goal is clear, it is not well understood how to go about achieving it. In this article we report on the use often class exercises in a Decision Support Systems course to promote higher order thinking skills in students. These class exercises improve student attendance, their understanding of the relevance of the course materials, and engage them in a process of analysis and evaluation which in tum sharpens their critical thinking skills. The instructor is also able to bring out details of complexities that are likely to be encountered in practice and discuss strategies that have worked in practice
Teaching about the Meaning and Importance of Quality in an Undergraduate Operations Management Course
Arup Mukherjee, Ph.D., is professor and chair, Management and Management Information Systems Department, University of West Florida, Pensacola, FL 32514
Several Trade off Features of Quantum Steering in Distributed Scenario
In the present work, we address the question of how bipartite steering
violation takes place among multi-partite systems (where each sub-system have
Hilbert space dimension restricted to two) based on the maximal violations of
the bipartite steering inequality of the reduced pairwise qubit systems. We
have derived a trade-off relation which is satisfied by those pairwise
bipartite maximal steering violations, which physically can be understood as
providing restrictions on the distribution of steering among subsystems. For a
three-qubit system, it is impossible that all pairs of qubits violate the
steering inequality, and once a pair of qubits violates the steering inequality
maximally, the other two pairs of qubits must both obey the steering
inequality. We also present a complementarity relation between genuine
entanglement present in a tripartite state and maximum bipartite steering
violation by its reduced states.Comment: Close to published versio
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