Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Risk of fatal injury in older adult drivers, passengers, and pedestrians

Objectives To compare risk of fatal injury in elderly road users (drivers, passengers, pedestrians) with that of younger age groups and to assess the contribution of elderly road users to the number of reported fatalities in the population. Design Fatality age was categorized as 21 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, or 70 and older, and road user was categorized as driver, passenger, or pedestrian. Estimated number of trips made by each age group was used to adjust for exposure and to measure individual risk. Setting Fatalities recorded in Britain between 1989 and 2009. Participants Population-wide fatal injury counts in Britain. Measurements Age of fatally injured drivers, passengers, and pedestrians. Estimated number of trips made per year by drivers, passengers, and pedestrians. Results Risk of fatal injury, but not fatality numbers in the population, were higher for older adult (=70) drivers than for younger age groups. Risk of fatal injury was also high for older adult passengers and pedestrians, who represented the majority of older adult fatalities. Conclusion Previous emphasis on driver impairment in older age has unduly focussed attention on elderly drivers, who represent a minority of all driver fatalities. Older adults represent a much larger proportion of passenger and pedestrian fatalities. Additional policy schemes and initiatives should be targeted at safeguarding older adult passengers and making the road environment safer for elderly pedestrians. © 2012, Copyright the Authors Journal compilation © 2012, The American Geriatrics Society.

Changes in natural killer cells, the CD57CD8 subset, and related cytokines in healthy aging

Aging has been shown to be accompanied by various changes in the lymphocyte subset distribution in the elderly. We have investigated more fully, and in a large number of subjects, age-related changes within several subpopulations bearing natural killer (NK) cell-associated surface antigens and changes in several cytokines involved in NK cell expansion. A total of 229 healthy subjects from all decades of life from 20 to 98 years of age was included in this cross-sectional study. A significant increase with age was found in both the absolute counts and the proportions of CD3-CD(16+56)+, CD3+CD(16+56)+, CD57+CD8+, CD57+CD8(low)+, and CD57+CD8- cells, whereas the CD57+CD8(high)+ subset, which may represent the cytolytic T cell population more precisely, showed less change with age. Some evidence is also provided to suggest that these expanded NK cell populations are in an activated state. Soluble IL-2 receptor levels were also found to increase significantly with age and correlated with certain NK cell subsets. Although the functions of some of these subsets remain to be elucidated, their expansion in the elderly may represent a remodeling of the immune system with increasing age, with an increase in non-MHC-restricted cells perhaps compensating for the previously reported decline in T and B cells in the elderly. Alternatively, increased numbers of these cells may be a direct result of cytokine dysregulation or increased antigenic or neoplastic cell challenge.

Effect of a multifaceted intervention on number of antimicrobial prescriptions for suspected urinary tract infections in residents of nursing homes:Cluster randomised controlled trial

Objective: To assess whether a multifaceted intervention can reduce the number of prescriptions for antimicrobials for suspected urinary tract infections in residents of nursing homes. Design: Cluster randomised controlled trial. Setting: 24 nursing homes in Ontario, Canada, and Idaho, United States. Participants: 12 nursing homes allocated to a multifaceted intervention and 12 allocated to usual care. Outcomes were measured in 4217 residents. Interventions: Diagnostic and treatment algorithm for urinary tract infections implemented at the nursing home level using a multifaceted approach-small group interactive sessions for nurses, videotapes, written material, outreach visits, and one on one interviews with physicians. Main outcome measures: Number of antimicrobials prescribed for suspected urinary tract infections, total use of antimicrobials, admissions to hospital, and deaths. Results: Fewer courses of antimicrobials for suspected urinary tract infections per 1000 resident days were prescribed in the intervention nursing homes than in the usual care homes (1.17 v 1.59 courses; weighted mean difference -0.49, 95% confidence intervals -0.93 to -0.06). Antimicrobials for suspected urinary tract infection represented 28.4% of all courses of drugs prescribed in the intervention nursing homes compared with 38.6% prescribed in the usual care homes (weighted mean difference -9.6%, -16.9% to -2.4%). The difference in total antimicrobial use per 1000 resident days between intervention and usual care groups was not significantly different (3.52 v 3.93; weighed mean difference -0.37, -1.17 to 0.44). No significant difference was found in admissions to hospital or mortality between the study arms. Conclusion: A multifaceted intervention using algorithms can reduce the number of antimicrobial prescriptions for suspected urinary tract infections in residents of nursing homes.

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.

Is the number of species on earth increasing or decreasing? Time, chaos and the origin of species

Darwin's On the Origin of Species has led to a theory of evolution with a mass of empirical detail on population genetics below species level, together with heated debate on the details of macroevolutionary patterns above species level. Most of the main principles are clear and generally accepted, notably that life originated once and has evolved over time by descent with modification. Here, I review the fossil and molecular phylogenetic records of the response of life on Earth to Quaternary climatic changes. I suggest that the record can be best understood in terms of the nonlinear dynamics of the relationship between genotype and phenotype, and between climate and environments. 'The origin of species' is essentially unpredictable, but is nevertheless an inevitable consequence of the way that organisms reproduce through time. The process is 'chaotic', but not 'random'. I suggest that biodiversity is best considered as continuously branching systems of lineages, where 'species' are the branch tips. The Earth's biodiversity should thus (1) be in a state of continuous increase and (2) show continuous discrepancies between genetic and morphological data in time and space. © The Palaeontological Association.

Modification of the formation of high-Mach number electrostatic shock-like structures by the ion acoustic instability

The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one- and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical plasma clouds, which consist of equally hot electrons and ions with a mass ratio of 250. The Mach number of the collision speed with respect to the initial ion acoustic speed of the plasma is set to 4.6. This high Mach number delays the formation of such structures by tens of inverse ion plasma frequencies. A pair of stable shock-like structures is observed after this time in the 1D simulation, which gradually evolve into electrostatic shocks. The ion acoustic instability, which can develop in the 2D simulation but not in the 1D one, competes with the nonlinear process that gives rise to these structures. The oblique ion acoustic waves fragment their electric field. The transition layer, across which the bulk of the ions change their speed, widens and their speed change is reduced. Double layer-shock hybrid structures develop.

Impact of the number of users on error probabilities in multiuser diversity systems

Multiuser diversity gain has been investigated well in terms of a system capacity formulation in the literature. In practice, however, designs on multiuser systems with nonzero error rates require a relationship between the error rates and the number of users within a cell. Considering a best-user scheduling, where the user with the best channel condition is scheduled to transmit per scheduling interval, our focus is on the uplink. We assume that each user communicates with the base station through a single-input multiple-output channel. We derive a closed-form expression for the average BER, and analyze how the average BER goes to zero asymptotically as the number of users increases for a given SNR. Note that the analysis of average BER even in SI SO multiuser diversity systems has not been done with respect to the number of users for a given SNR. Our analysis can be applied to multiuser diversity systems with any number of antennas.

Dynamical symmetry breaking with optimal control: Reducing the number of pieces

We analyze the production of defects during the dynamical crossing of a mean-field phase transition with a real order parameter. When the parameter that brings the system across the critical point changes in time according to a power-law schedule, we recover the predictions dictated by the well-known Kibble-Zurek theory. For a fixed duration of the evolution, we show that the average number of defects can be drastically reduced for a very large but finite system, by optimizing the time dependence of the driving using optimal control techniques. Furthermore, the optimized protocol is robust against small fluctuations.

Cyanoacrylate glue versus suture in peripheral nerve reanastomosis

OBJECTIVE: To assess the effectiveness of n-butyl-2-cyanoacrylate glue compared with microsuturing technique in peripheral nerve reanastomosis in rats.

STUDY DESIGN: Fourteen young adult white rats were used. Bilateral sciatic neurotomies were performed in 12 of them and then reanastomosed with 3 epineural microsutures in the right side (study group G1) and with n-butyl-2-cyanoacrylate glue in the left side (study group G2). On the remaining 2 rats (control group G3), sham surgery was done on both sides. Biopsies were harvested 12 weeks after surgery and examined under light microscope using Osmic acid stains. The number of nerve fibers was counted in the distal and proximal nerve segments, and the results were analyzed and compared in all groups.

RESULTS: Adequate regeneration with no anastomotic ruptures was seen 12 weeks after surgery in G1 and G2. The histomorphometric assessment showed no statistically significant difference (P = .960) in the neurotization index of G1 (89.01%) compared with G2 (88.97%). There was a significant (P = .001) reduction in the mean number of axon counts distal to the repair in G1 (271.3) and G2 (272.8) compared with that of the proximal segments of each study group (304.6 and 303, respectively, as well as to that of G3 (348.5).

CONCLUSION: Both n-butyl-2-cyanoacrylate adhesive and 3-microsuture techniques showed comparable neurotization indices and were equally adequate to stabilize the nerve during regeneration period.