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.

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.

Discovering subgroups of patients from DNA copy number data using NMF on compacted matrices

In the study of complex genetic diseases, the identification of subgroups of patients sharing similar genetic characteristics represents a challenging task, for example, to improve treatment decision. One type of genetic lesion, frequently investigated in such disorders, is the change of the DNA copy number (CN) at specific genomic traits. Non-negative Matrix Factorization (NMF) is a standard technique to reduce the dimensionality of a data set and to cluster data samples, while keeping its most relevant information in meaningful components. Thus, it can be used to discover subgroups of patients from CN profiles. It is however computationally impractical for very high dimensional data, such as CN microarray data. Deciding the most suitable number of subgroups is also a challenging problem. The aim of this work is to derive a procedure to compact high dimensional data, in order to improve NMF applicability without compromising the quality of the clustering. This is particularly important for analyzing high-resolution microarray data. Many commonly used quality measures, as well as our own measures, are employed to decide the number of subgroups and to assess the quality of the results. Our measures are based on the idea of identifying robust subgroups, inspired by biologically/clinically relevance instead of simply aiming at well-separated clusters. We evaluate our procedure using four real independent data sets. In these data sets, our method was able to find accurate subgroups with individual molecular and clinical features and outperformed the standard NMF in terms of accuracy in the factorization fitness function. Hence, it can be useful for the discovery of subgroups of patients with similar CN profiles in the study of heterogeneous diseases.