Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Organizational assessment in paediatric primary care:Development and initial validation of the primary care organizational questionnaire

Primary care in the United States is undergoing many changes. Reliable and valid instruments are needed to assess the effects of these changes. The Primary Care Organizational Questionnaire (PCOQ), a 56-item 5-point Likert scale survey that evaluates interactions among members of the clinic/practice and job-related attributes, was administered to clinicians and staff in 36 primary care practices serving paediatric populations in Connecticut. A priori scales were reliable (Cronbach alpha =0.7). Analysis of variance (ANOVA) showed greater heterogeneity across clinics than within clinics for 13 of 15 a priori scales, which were then included in a principal component factor analysis with varimax rotation. Eigenvalue analysis showed nine significant factors, largely similar to the a priori scales, indicating concurrent construct validity. Further research will ascertain the utility of the PCOQ in predicting the effectiveness of primary care practices in implementing disease management programmes. © 2006 Royal Society of Medicine Press.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Novel Generic Bounds on the Sum Rate of MIMO ZF Receivers

This paper introduces some novel upper and lower bounds on the achievable sum rate of multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receivers. The presented bounds are not only tractable but also generic since they apply for different fading models of interest, such as uncorrelated/ correlated Rayleigh fading and Ricean fading. We further formulate a new relationship between the sum rate and the first negative moment of the unordered eigenvalue of the instantaneous correlation matrix. The derived expressions are explicitly compared with some existing results on MIMO systems operating with optimal and minimum mean-squared error (MMSE) receivers. Based on our analytical results, we gain valuable insights into the implications of the model parameters, such as the number of antennas, spatial correlation and Ricean-K factor, on the sum rate of MIMO ZF receivers. © 2011 IEEE.

Analysis of Load Impact on Small-signal Stability based on Load Active Power Sensitivity

While load flow conditions vary with different loads, the small-signal stability of the entire system is closely related with to the locations, capacities and models of loads. In this paper, load impacts with different capacities and models on the small-signal stability are analysed. In the real large-scale power system case, the load sensitivity which denotes the sensitivity of the eigenvalue with respect to the load active power is introduced and applied to rank the loads. The loads with high sensitivity are also considered.

Xheal: A localized self-healing algorithm using expanders

We consider the problem of self-healing in reconfigurable networks e.g., peer-to-peer and wireless mesh networks. For such networks under repeated attack by an omniscient adversary, we propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, while keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Xheal has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] andForgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.

Small Signal Stability Performance of Power System during High Penetration of Wind Generation

The small signal stability of interconnected power systems is one of the important aspects that need to be investigated since the oscillations caused by this kind of instability have caused many incidents. With the increasing penetration of wind power in the power system, particularly doubly fed induction generator (DFIG), the impact on the power system small signal stability performance should be fully investigated. Because the DFIG wind turbine integration is through a fast action converter and associated control, it does not inherently participate in the electromechanical small signal oscillation. However, it influences the small signal stability by impacting active power flow paths in the network and replacing synchronous generators that have power system stabilizer (PSS). In this paper, the IEEE 39 bus test system has been used in the analysis. Furthermore, four study cases and several operation scenarios have been conducted and analysed. The selective eigenvalue Arnoldi/lanczos's method is used to obtain the system eigenvalue in the range of frequency from 0.2 Hz to 2 Hz which is related to electromechanical oscillations. Results show that the integration of DFIG wind turbines in a system during several study cases and operation scenarios give different influence on small signal stability performance.

Android Malware Detection: an Eigenspace Analysis Approach

The battle to mitigate Android malware has become more critical with the emergence of new strains incorporating increasingly sophisticated evasion techniques, in turn necessitating more advanced detection capabilities. Hence, in this paper we propose and evaluate a machine learning based approach based on eigenspace analysis for Android malware detection using features derived from static analysis characterization of Android applications. Empirical evaluation with a dataset of real malware and benign samples show that detection rate of over 96% with a very low false positive rate is achievable using the proposed method.

Identification of Small Signal Oscillation Mode Parameters from Simulated and Actual PMU Ringdown Data

This paper presents the practical use of Prony Analysis to identify small signal oscillation mode parameters from simulated and actual phasor measurement unit (PMU) ringdown data. A well-known two-area four-machine power system was considered as a study case while the latest PMU ringdown data were collected from a double circuit 275 kV main interconnector on the Irish power system. The eigenvalue analysis and power spectral density were also conducted for the purpose of comparison. The capability of Prony Analysis to identify the mode parameters from three different types of simulated PMU ringdown data has been shown successfully. Furthermore, the results indicate that the Irish power system has dominant frequency modes at different frequencies. However, each mode has good system damping.