On the Cardinality of Positively Linearly Independent Sets

Positive bases, which play a key role in understanding derivative free optimization methods that use a direct search framework, are positive spanning sets that are positively linearly independent. The cardinality of a positive basis in $\R^n$ has been established to be between $n+1$ and $2n$ (with both extremes existing). The lower bound is immediate from being a positive spanning set, while the upper bound uses {\em both} positive spanning and positively linearly independent. In this note, we provide details proving that a positively linearly independent set in $\R^n$ for $n \in \{1, 2\}$ has at most $2n$ elements, but a positively linearly independent set in $\R^n$ for $n\geq 3$ can have an arbitrary number of elements

The Political Economy of Growth and Governance

There are diverse ideas about governance around the world, and this paper studies them through the following questions: (a) what does the available evidence tell us about the political and institutional requirements for sustained economic growth? (b) What do we need from the state to secure growth? (c) How do a country’s internal characteristics support or impede its growth? (d) How does the external environment of a country influence its economic growth prospects? These elements are then put together into a model of growth, from which we derive conclusions about governance arrangements. Thus the paper outlines a simple framework within which to think about the political economy of growth that can be summed up in five points: good government, with secure political conditions; credible macroeconomic stability; savings and investment high enough to sustain adequate growth; openness to the world economy; and the discipline of external engagement. It then argues that the growth model needs to be underpinned by suitable governance arrangements, and suggests that good governance has two main elements, each quite complex in practice, namely: protection of property rights, and accountability of government.political economy, global economy, economic growth, governance, macroeconomic stability, property rights

Effecting institutional change: The impact of some strategic issues on the integratiye use of IT in teaching and learning

This paper addresses the effective implementation of change through the identification of issues associated with three key institutional areas which, together, will ensure the effective'integration of multimedia technologies into teaching and learning. These are the need for a firm commitment of support at the institutional level, the development of an institutional strategy, with related staff‐development policies and programmes, and provision for students and academic staff to. acquire enabling IT skills through resource‐based learning as a means to maximize the benefits to be gained from the use of these new technologies. The essential conditions which ensure effective implementation ‐ communication between all stake‐holders, leadership by senior managers, responsive central services and a mixture of funding arrangements ‐ are discusse

Smoothness of convolution products of orbital measures on rank one compact symmetric spaces

We prove that all convolution products of pairs of continuous orbital measures in rank one, compact symmetric spaces are absolutely continuous and determine which convolution products are in $L^{2}$ (meaning, their density function is in $L^{2})$. Characterizations of the pairs whose convolution product is either absolutely continuous or in $L^2$ are given in terms of the dimensions of the corresponding double cosets. In particular, we prove that if $G/K$ is not $SU(2)/SO(2),$ then the convolution of any two regular orbital measures is in $L^{2}$, while in $SU(2)/SO(2)$ there are no pairs of orbital measures whose convolution product is in $L^{2}$

Efficacy of Continuous Passive Motion after Total Knee Arthroplasty in Veteran Patients

Since the early 1980s, continuous passive motion has been used as adjunct therapy in patients’ rehabilitation following total knee arthroplasty. Although existing literature challenged the benefits of continuous passive motion claiming it had no added short-term or long-term benefits after knee arthroplasty (Boese et al., 2014; Chen et al., 2012; Herbold et al., 2014; Leach et al., 2006; Maniar et al., 2012), the existing literature is difficult to generalize and apply to the veteran population at San Francisco Veterans Affairs Medical Center. This study was undertaken to determine the efficacy of continuous passive motion in helping veteran patients at San Francisco Veterans Affairs Medical Center achieve post-operative range of motion goals following total knee arthroplasty. Using a retrospective design an extensive chart review was conducted. Analysis of Variance (ANOVA) with time as a repeated measure independent variable, continuous passive motion as a between-subjects independent variable, and extension/flexion as dependent variables was conducted. For extension, time was statistically significant (p \u3c .001) but mean extension did not differ between continuous passive motion and no continuous passive motion (p = .976). Similarly, for flexion, time was statistically significant (p \u3c .001) but mean flexion did not differ between continuous passive motion and no continuous passive motion (p = .128). Therefore, this research is consistent with current literature, which claims that continuous passive motion does not have short-term benefits, particularly in the area of range of motion

Semantic Retrieval and Automatic Annotation: Linear Transformations, Correlation and Semantic Spaces

This paper proposes a new technique for auto-annotation and semantic retrieval based upon the idea of linearly mapping an image feature space to a keyword space. The new technique is compared to several related techniques, and a number of salient points about each of the techniques are discussed and contrasted. The paper also discusses how these techniques might actually scale to a real-world retrieval problem, and demonstrates this though a case study of a semantic retrieval technique being used on a real-world data-set (with a mix of annotated and unannotated images) from a picture library