Loss of correlation between HIV viral load and CD4+ T-cell counts in HIV/HTLV-1 co-infection in treatment naive Mozambican patients

Seven hundred and four HIV-1/2-positive, antiretroviral therapy (ART) naïve patients were screened for HTLV-1 infection. Antibodies to HTLV-1 were found in 32/704 (4.5%) of the patients. Each co-infected individual was matched with two HIV mono-infected patients according to World Health Organization clinical stage, age +/-5 years and gender. Key clinical and laboratory characteristics were compared between the two groups. Mono-infected and co-infected patients displayed similar clinical characteristics. However, co-infected patients had higher absolute CD4+ T-cell counts (P = 0.001), higher percentage CD4+ T-cell counts (P < 0.001) and higher CD4/CD8 ratios (P < 0.001). Although HIV plasma RNA viral loads were inversely correlated with CD4+ T-cell-counts in mono-infected patients (P < 0.0001), a correlation was not found in co-infected individuals (P = 0.11). Patients with untreated HIV and HTLV-1 co-infection show a dissociation between immunological and HIV virological markers. Current recommendations for initiating ART and chemoprophylaxis against opportunistic infections in resource-poor settings rely on more readily available CD4+ T-cell counts without viral load parameters. These guidelines are not appropriate for co-infected individuals in whom high CD4+ T-cell counts persist despite high HIV viral load states. Thus, for co-infected patients, even in resource-poor settings, HIV viral loads are likely to contribute information crucial for the appropriate timing of ART introduction

On the Complexity of Searching in Trees: Average-case Minimization

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little was known about this natural question and the complexity of the problem had remained so far an open question. We close this question and prove that the above tree search problem is NP-complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In fact, for diameter not larger than 3 the problem can be shown to be polynomially solvable using a dynamic programming approach. In addition we prove that the problem is NP-complete even for the class of trees of maximum degree at most 16. To the best of our knowledge, the only known result in this direction is that the tree search problem is solvable in O(|V| log|V|) time for trees with degree at most 2 (paths). We match the above complexity results with a tight algorithmic analysis. We first show that a natural greedy algorithm attains a 2-approximation. Furthermore, for the bounded degree instances, we show that any optimal strategy (i.e., one that minimizes the expected number of queries) performs at most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum degree of T. We combine this result with a non-trivial exponential time algorithm to provide an FPTAS for trees with bounded degree

Some combinatorial identities related to commuting varieties and Hilbert schemes

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane

Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers

The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a set of deformed Stirling numbers which replace the Stirling numbers occurring in the conventional case. On the other hand, the deformed Stirling numbers which have to be introduced in the case of the `P-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = q^{-\hat{n}}$, are found to depend on the operator $\hat{n}$. This distinction between the two types of deformed bosons is in harmony with earlier observations made in the context of a study of the extended Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Team-based learning (TBL): a community of practice

Background Rapid changes in medical practice have a large impact on the demands faced by educators in preparing students for future participation in a multifaceted healthcare workforce. Competencies required by today’s medical graduates encompass the ability to effectively collaborate, communicate and problem solve. The learning needs of medical students have also changed over time. Today’s medical students are highly interconnected, enjoying teamwork and collaborative practice, and desire continuous, explicit feedback. They want structured learning activities, with clear expectations, and enjoy a sense of accomplishment on their achievements. The conflation of these issues has seen many medical schools adopt the model of Team-based learning (TBL). Using the conceptual framework of communities of practice, we sought to qualitatively explore students’ and teachers’ experience of TBL in Year 1 of a graduate entry medical program. Methods Convenience sampling was used to select 169/350 (48%) Year 1 students who completed three TBL sessions. Each TBL session was facilitated by three senior clinicians. Following participation in the TBLs, students were invited to attend focus groups, and all facilitators (n = 9) were invited to attend interviews. A coding framework was developed to code the entire dataset, using the theoretical lens of communities of practice. Results 34/169 (20%) of students attended focus groups. Three facilitators (3/9, 33%) were interviewed. Students and facilitators felt the structure and organisation of TBL made students accountable for their learning and team contributions. The combined expertise and clinical experience of facilitators, with immediate feedback helped groups to work both independently and collaboratively. Facilitators found working with their peers in the TBLs to be a rewarding experience. Conclusions The community of practice found in the TBL classes, provided an enriching and rewarding learning environment that motivated students to build on their basic knowledge and apply what had been learnt. The interactions of experienced, senior clinicians as facilitators, sharing their expertise within a clinical context, prompted effective student engagement in learning and understanding. Our change in curriculum design and pedagogy will assist in preparing medical students for demands of the increasingly complex healthcare systems in which they will work

Operator renewal theory and mixing rates for dynamical systems with infinite measure

We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer operator. This was previously an intractable problem. Examples of systems covered by our results include (i) parabolic rational maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly expanding interval maps with indifferent fixed points. In addition, we give a particularly simple proof of pointwise dual ergodicity (asymptotic behaviour of $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ and rates of mixing. Also, we obtain error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated version includes minor corrections in Sections 10 and 11, and corresponding modifications of certain statements in Section 1. All main results are unaffected. In particular, Sections 2-9 are unchanged from the published versio