Large deviations for eigenvalues of sample covariance matrices, with applications to mobile communication systems

We study sample covariance matrices of the form $W=\frac 1n C C^T$, where $C$ is a $k\times n$ matrix with i.i.d. mean zero entries. This is a generalization of so-called Wishart matrices, where the entries of $C$ are independent and identically distributed standard normal random variables. Such matrices arise in statistics as sample covariance matrices, and the high-dimensional case, when $k$ is large, arises in the analysis of DNA experiments. We investigate the large deviation properties of the largest and smallest eigenvalues of $W$ when either $k$ is fixed and $n\to \infty$, or $k_n\to \infty$ with $k_n=o(n/\log\log{n})$, in the case where the squares of the i.i.d. entries have finite exponential moments. Previous results, proving a.s. limits of the eigenvalues, only require finite fourth moments. Our most explicit results for $k$ large are for the case where the entries of $C$ are $\pm1$ with equal probability. We relate the large deviation rate functions of the smallest and largest eigenvalue to the rate functions for independent and identically distributed standard normal entries of $C$. This case is of particular interest, since it is related to the problem of the decoding of a signal in a code division multiple access system arising in mobile communication systems. In this example, $k$ plays the role of the number of users in the system, and $n$ is the length of the coding sequence of each of the users. Each user transmits at the same time and uses the same frequency, and the codes are used to distinguish the signals of the separate users. The results imply large deviation bounds for the probability of a bit error due to the interference of the various users.Comment: corrected some typing errors, and extended Theorem 3.1 to Wishart matrices; to appear in Advances of Applied Probabilit

Metabolic modeling of Chlamydomonas reinhardtii: energy requirements for photoautotrophic growth and maintenance

In this study, a metabolic network describing the primary metabolism of Chlamydomonas reinhardtii was constructed. By performing chemostat experiments at different growth rates, energy parameters for maintenance and biomass formation were determined. The chemostats were run at low irradiances resulting in a high biomass yield on light of 1.25 g  mol−1. The ATP requirement for biomass formation from biopolymers (Kx) was determined to be 109 mmol g−1 (18.9 mol mol−1) and the maintenance requirement (mATP) was determined to be 2.85 mmol g−1 h−1. With these energy requirements included in the metabolic network, the network accurately describes the primary metabolism of C. reinhardtii and can be used for modeling of C. reinhardtii growth and metabolism. Simulations confirmed that cultivating microalgae at low growth rates is unfavorable because of the high maintenance requirements which result in low biomass yields. At high light supply rates, biomass yields will decrease due to light saturation effects. Thus, to optimize biomass yield on light energy in photobioreactors, an optimum between low and high light supply rates should be found. These simulations show that metabolic flux analysis can be used as a tool to gain insight into the metabolism of algae and ultimately can be used for the maximization of algal biomass and product yield

Heavy menstrual bleeding on direct factor Xa inhibitors: Rationale and design of the MEDEA study

Background: In premenopausal women, treatment with direct oral factor Xa inhibitors is associated with an increased risk of heavy menstrual bleeding (HMB) compared with vitamin K antagonists (VKA). Treatment with the direct oral thrombin inhibitor dabigatran appears to be associated with a reduced risk of HMB compared with VKA. These findings come from small observational studies or post hoc analyses of trials in which HMB was not a primary outcome. Use of tranexamic acid during the menstrual period may be effective in patients with HMB, but prospective data regarding efficacy and safety in patients on anticoagulant treatment are lacking. Rationale and Design: A direct comparison of a factor Xa inhibitor and a thrombin inhibitor with HMB as primary outcome, as well as an evaluation of the effects of adding tranexamic acid in women with anticoagulant-associated HMB is highly relevant for clinical practice. The MEDEA study is a randomized, open-label, pragmatic clinical trial to evaluate management strategies in premenopausal women with HMB associated with factor Xa inhibitor therapy. Outcomes: Women using factor Xa inhibitors with proven HMB, as assessed by a pictorial blood loss assessment chart (PBAC) score of >150, will be randomized to one of three study arms: (i) switch to dabigatran; (ii) continue factor Xa inhibitor with addition of tranexamic acid during the menstrual period; or (iii) continue factor Xa inhibitor without intervention. The primary outcome is the difference in PBAC score before and after randomization. Here, we present the rationale and highlight several unique features in the design of the study

Linear Interference Cancellation in CDMA Systems and Large Deviations of the Correlation Matrix Eigenvalues

Abstract We analytically compute a measure of performance of various linear Parallel Interference Cancellation (PIC) decoding schemes in the infinite stage limit, for moderately loaded CDMA systems without AWGN, or with a sufficiently small amount of AWGN. This measure is the exponential rate of the BEP, which does not involve Gaussian approximations. We obtain these rates using large deviation theory for the eigenvalues of the code correlation matrix. We find that the decorrelator performs best, followed by infinitestage SD-PIC, which is found to perform better than infinite stage HD-PIC

Satisfaction and quality of life in women who undergo breast surgery: A qualitative study

Background. In cosmetic and reconstructive breast surgery, measurement of patient-reported outcomes has become increasingly important to research efforts and clinical care. We aimed to describe how breast conditions and breast surgery impact on patient satisfaction and quality of life. Methods We conducted qualitative, in-depth interviews with 48 women who had undergone either breast reduction (n = 15), breast augmentation (n = 12), or breast reconstruction (n = 21) surgery in order to begin to build a theoretical understanding of patient satisfaction and quality of life in breast surgery patients. Interviews were audio-taped, transcribed verbatim and analyzed thematically. Results The patient interviews revealed that breast conditions and breast surgery impact women in the following six main areas: satisfaction with breasts; satisfaction with overall outcome; psychosocial well-being; sexual well-being; physical well-being; and satisfaction with the process of care. We used these six themes to form the basis of a conceptual framework of patient satisfaction and quality of life in women who undergo breast surgery. Conclusion Our conceptual framework establishes the main issues of concern for breast surgery patients. This new framework can be used to help develop local guidelines for future clinical assessment, management and measurement, establish the validity of the current management strategies, and develop evidence-based guidance for the development of new patient reported outcome measures for future outcomes research.Medicine, Faculty ofNon UBCReviewedFacult

Microalgal triacylglycerides production in outdoor batch-operated tubular PBRs

Background: Microalgal triacylglycerides (TAGs) are a promising sustainable feedstock for the biofuel, chemical and food industry. However, industrial production of microalgal products for commodity markets is not yet economically viable, largely because of low microalgal productivity. The latter is strictly dependent on initial-biomass-specific (IBS) light availability (i.e. ratio of light impinging on reactor ground area divided by initial biomass concentration per ground area). This study investigates the effect of IBS-light availability on batch TAG production for Nannochloropsis sp. cultivated in two outdoor tubular reactors (i.e. vertical and horizontal) at different initial biomass concentrations for the TAG accumulation phase, during two distinct seasons (i.e. high and low light conditions). Results: Increasing IBS-light availability led to both a higher IBS-TAG production rate and TAG content at the end of the batch, whereas biomass yield on light decreased. As a result, an optimum IBS-light availability was determined for the TAG productivity obtained at the end of the batch and several guidelines could be established. The vertical reactor (VR) should be operated at an initial biomass concentration of 1.5 g L-1 to achieve high TAG productivities (1.9 and 3.2 g m-2 day-1 under low and high light, respectively). Instead, the horizontal reactor (HR) should be operated at 2.5 g L-1 under high light (2.6 g m-2 day-1), and at 1.5 g L-1 under low light (1.4 g m-2 day-1). Conclusions: From this study, the great importance of IBS-light availability on TAG production can be deduced. Although maintaining high light availabilities in the reactor is key to reach high TAG contents at the end of the batch, considerable losses in TAG productivity were observed for the two reactors regardless of light condition, when not operated at optimal initial biomass concentrations (15-40% for VR and 30-60% for HR).</p