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.

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.

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.

Shared decision making in patients at risk of cancer: The role of domain and numeracy

Background
Shared decision making has become an integral part of medical consultation. Research has, however, reported wide differences in individuals' desires to be involved in the decision-making process, and these differences in preferences are likely to be the result of a number of factors including age, education and numeracy.

Objective
To investigate whether patients at genetic risk for cancer had preferences for shared decision making that differed depending on medical domain (general health vs. cancer) and whether decision preferences are linked to numeracy abilities.

Methods
Four hundred and seventy-six women who consented to participate in response to an email sent by a local branch of the U.S.-based Cancer Genetics Network (CGN) to its members. Participants completed the Control Preference Scale, as well as an objective and subjective numeracy scales.

Results
Decision domain (cancer vs. general health) was not associated with women's preferences for involvement in decision making. Objective and subjective numeracy predicted a preference for decision involvement in general, and only objective numeracy was predictive with regard to cancer.

Conclusion
Participants were equally likely to state they wanted to play an active, collaborative or passive role in both medical domains (general and cancer). High-numeracy participants were more likely to express a desire for an active role in general and in case they were diagnosed with cancer.

Practice implications
Health authorities' recommendations to clinicians to include patients in their medical decisions are supported by patients' desires, and clinicians should be cognizant of their patients' preferences as well as their numeracy skills.