Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

A low overhead error confinement method based on application statistical characteristics

Reliability has emerged as a critical design constraint especially in memories. Designers are going to great lengths to guarantee fault free operation of the underlying silicon by adopting redundancy-based techniques, which essentially try to detect and correct every single error. However, such techniques come at a cost of large area, power and performance overheads which making many researchers to doubt their efficiency especially for error resilient systems where 100% accuracy is not always required. In this paper, we present an alternative method focusing on the confinement of the resulting output error induced by any reliability issues. By focusing on memory faults, rather than correcting every single error the proposed method exploits the statistical characteristics of any target application and replaces any erroneous data with the best available estimate of that data. To realize the proposed method a RISC processor is augmented with custom instructions and special-purpose functional units. We apply the method on the proposed enhanced processor by studying the statistical characteristics of the various algorithms involved in a popular multimedia application. Our experimental results show that in contrast to state-of-the-art fault tolerance approaches, we are able to reduce runtime and area overhead by 71.3% and 83.3% respectively.

Mental Health and Morbidity of Caregivers and Co-Residents of individuals with Dementia: A Quasi-Experimental Design

Objectives: To determine if providing informal care to a co-resident with dementia symptoms places an additional risk on the likelihood of poor mental health or mortality compared to co-resident non-caregivers.
Design: A quasi-experimental design of caregiving and non-caregiving co-residents of individuals with dementia symptoms, providing a natural comparator for the additive effects of caregiving on top of living with an individual with dementia symptoms. 
Methods: Census records, providing information on household structure, intensity of caregiving, presence of dementia symptoms and self-reported mental health, were linked to mortality records over the following 33 months. Multi-level regression models were constructed to determine the risk of poor mental health and death in co-resident caregivers of individuals with dementia symptoms compared to co-resident non-caregivers, adjusting for the clustering of individuals within households.
Results: The cohort consisted of 10,982 co-residents (55.1% caregivers), with 12.1% of non-caregivers reporting poor mental health compared to 8.4% of intense caregivers (>20 hours of care per week). During follow-up the cohort experienced 560 deaths (245 to caregivers). Overall, caregiving co-residents were at no greater risk of poor mental health but had lower mortality risk than non-caregiving co-residents (ORadj=0.93, 95% CI 0.79, 1.10 and ORadj=0.67, 95% CI 0.56, 0.81, respectively); this lower mortality risk was also seen amongst the most intensive caregivers (ORadj=0.65, 95% CI 0.53, 0.79).
Conclusion: Caregiving poses no additional risk to mental health over and above the risk associated with merely living with someone with dementia, and is associated with a lower mortality risk compared to non-caregiving co-residents.

The Last Minutes of Oxygen Shell Burning in a Massive Star

We present the first 3D simulation of the last minutes of oxygen shell burning in an 18 solar mass supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a 1D stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ~0.1 at collapse, and an l=2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51 to 0.56 solar masses due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12--24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.