A Cough-Based Algorithm for Automatic Diagnosis of Pertussis

Pertussis is a contagious respiratory disease which mainly affects young children and can be fatal if left untreated. The World Health Organization estimates 16 million pertussis cases annually worldwide resulting in over 200,000 deaths. It is prevalent mainly in developing countries where it is difficult to diagnose due to the lack of healthcare facilities and medical professionals. Hence, a low-cost, quick and easily accessible solution is needed to provide pertussis diagnosis in such areas to contain an outbreak. In this paper we present an algorithm for automated diagnosis of pertussis using audio signals by analyzing cough and whoop sounds. The algorithm consists of three main blocks to perform automatic cough detection, cough classification and whooping sound detection. Each of these extract relevant features from the audio signal and subsequently classify them using a logistic regression model. The output from these blocks is collated to provide a pertussis likelihood diagnosis. The performance of the proposed algorithm is evaluated using audio recordings from 38 patients. The algorithm is able to diagnose all pertussis successfully from all audio recordings without any false diagnosis. It can also automatically detect individual cough sounds with 92% accuracy and PPV of 97%. The low complexity of the proposed algorithm coupled with its high accuracy demonstrates that it can be readily deployed using smartphones and can be extremely useful for quick identification or early screening of pertussis and for infection outbreaks control

Mixed Hodge polynomials of character varieties

We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)-character variety. The calculation also leads to several conjectures about the cohomology of M_n: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n = 2.Comment: with an appendix by Nicholas M. Katz; 57 pages. revised version: New definition for homogeneous weight in Definition 4.1.6, subsequent arguments modified. Some other minor changes. To appear in Invent. Mat

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Three-variable Mahler measures and special values of modular and Dirichlet LL-series

In this paper we prove that the Mahler measures of the Laurent polynomials $(x+x^{-1})(y+y^{-1})(z+z^{-1})+k$, $(x+x^{-1})^2(y+y^{-1})^2(1+z)^3z^{-2}-k$, and $x^4+y^4+z^4+1+k^{1/4}xyz$, for various values of $k$, are of the form $r_1 L'(f,0)+r_2 L'(\chi,-1)$, where $r_1,r_2\in \mathbb{Q}$, $f$ is a CM newform of weight 3, and $\chi$ is a quadratic character. Since it has been proved that these Maher measures can also be expressed in terms of logarithms and $_5F_4$-hypergeometric series, we obtain several new hypergeometric evaluations and transformations from these results

Using Genetic Diversity in Deep Root Systems of Perennial Forage Grasses and Rice to Capture Carbon in Tropical Soils

Agricultural soils have the potential not only to be sinks of carbon dioxide (CO2) but also to mitigate the emissions of this gas to the atmosphere, thus, alleviating global warming. Perennial tropical grasses and rice upland and lowland varieties exhibit a large untapped genetic diversity in their root systems (e.g., deep rooting ability, exudation rates and chemical composition) that, if unlocked, could contribute to increased food production in crop-livestock systems while enhancing soil organic carbon (SOC) in tropical regions. Naturebased solutions that improve crop adaptation and SOC storage in tropical soils could help to remove CO2 from the atmosphere and thereby benefit the global climate system. With the launch of Future Seeds, one of the world’s largest repositories of tropical crop varieties, the Bezos Earth Fund (BEF) granted a major project within the Program of Future of Food. The focus of this BEF funded project is to: (i) develop novel high-throughput phenotyping methods to evaluate genetic diversity of root systems of tropical grasses and rice; (ii) unravel the potential of root systems in crop-livestock systems to replenish soil organic carbon (SOC) in human-intervened areas in tropical soils; (iii) identify and target hotspots/agroecological niches for SOC storage in tropical soils; and (iv) build capacity in conducting research on root systems and SOC storage towards carbon farming in tropical regions. Implementation of land-based SOC storage practices/projects (through carbon markets) based on deep rooting ability of perennial tropical forage grasses and rice cultivars in crop-pasture rotational systems could significantly reduce net emissions from tropical soils

Using principal component analysis to develop a single-parameter screening tool for metabolic syndrome

Abstract Background Metabolic syndrome (MS) is an important current public health problem faced worldwide. To prevent an "epidemic" of this syndrome, it is important to develop an easy single-parameter screening technique (such as waist circumference (WC) determination recommended by the International Diabetes Federation). Previous studies proved that age is a chief factor corresponding to central obesity. We intended to present a new index based on the linear combination of body mass index, and age, which could enhance the area under the receiver operating characteristic curves (AUCs) for assessing the risk of MS. Methods The labour law of the Association of Labor Standard Law, Taiwan, states that employers and employees are respectively obligated to offer and receive routine health examination periodically. Secondary data analysis and subject's biomarkers among five high-tech factories were used in this study between 2007 and 2008 in northern Taiwan. The subjects included 4712 males and 4196 females. The first principal component score (FPCS) and equal-weighted average (EWA) were determined by statistical analysis. Results Most of the metabolic and clinical characteristics were significantly higher in males than in females, except high-density lipoprotein cholesterol level. The older group (>45 years) had significantly lower values for height and high-density lipoprotein cholesterol level than the younger group. The AUCs of FPCS and EWA were significantly larger than those of WC and waist-to-height ratio. The low specificities of EWA and FPCS were compensated for by their substantially high sensitivities. FPCS ≥ 0.914 (15.4%) and EWA ≥ 8.8 (6.3%) were found to be the most prevalent cut off points in males and females, respectively. Conclusions The Bureau of Health Promotion, Department of Health, Taiwan, had recommended the use of WC ≥ 90 cm for males and ≥ 80 cm for females as singular criteria for the determination of central obesity instead of multiple parameters. The present investigation suggests that FPCS or EWA is a good predictor of MS among the Taiwanese. However, the use of FPCS is not computationally feasible in practice. Therefore, we suggest that EWA be used in clinical practice as a simple parameter for the identification of those at risk of MS.</p

Intravitreal bevacizumab (Avastin®) for diabetic retinopathy at 24-months: The 2008 Juan Verdaguer-planas lecture

Diabetic retinopathy (DR) remains the major threat to sight in the working age population. Diabetic macular edema (DME) is a manifestation of DR that produces loss of central vision. Proliferative diabetic retinopathy (PDR) is a major cause of visual loss in diabetic patients. In PDR, the growth of new vessels is thought to occur as a result of vascular endothelial growth factor (VEGF) release into the vitreous cavity as a response to ischemia. Furthermore, VEGF increases vessel permeability leading to deposition of proteins in the interstitium that facilitate the process of angiogenesis and macular edema. This review demonstrates multiple benefits of intravitreal bevacizumab (IVB) on DR including DME and PDR at 24 months of follow up. The results indicate that IVB injections may have a beneficial effect on macular thickness and visual acuity (VA) in diffuse diabetic macular edema. Therefore, in the future this new therapy could replace or complement focal/grid laser photocoagulation in DME. In PDR, this new option could be an adjuvant agent to pan-retina photocoagulation so that more selective therapy may be applied. In addition, we report a series of patients in which tractional retinal detachment developed or progressed after adjuvant preoperative IVB in severe PDR. © 2010 Bentham Science Publishers Ltd

Diagnostic Accuracy of Adenosine Deaminase and Lymphocyte Proportion in Pleural Fluid for Tuberculous Pleurisy in Different Prevalence Scenarios

BACKGROUND: Tuberculous pleural effusion (TPE) is a paucibacillary manifestation of tuberculosis, so isolation of Mycobacterium tuberculosis is difficult, biomarkers being an alternative for diagnosis. Adenosine deaminase (ADA) is the most cost-effective pleural fluid marker and is routinely used in high prevalence settings, whereas its value is questioned in areas with low prevalence. The lymphocyte proportion (LP) is known to increase the specificity of ADA for this diagnosis. We analyse the diagnostic usefulness of ADA alone and the combination of ADA ≥ 40 U/l (ADA(40)) and LP ≥ 50% (LP(50)) in three different prevalence scenarios over 11 years in our area. MATERIALS AND METHODS: Biochemistry, cytology and microbiology studies from 472 consecutive pleural fluid samples were retrospectively analyzed. ADA and differential cell count were determined in all samples. We established three different prevalence periods, based on percentage of pleural effusion cases diagnosed as tuberculosis: 1998-2000 (31.3%), 2001-2004 (11.8%), and 2005-2008 (7.4%). ROC curves, dispersion diagrams and pre/post-test probability graphs were produced. TPE accounted for 73 episodes (mean prevalence: 15.5%). The sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) for ADA(40) were 89%, 92.7%, 69.2% and 97.9%, respectively. For ADA(40)+LP(50) the specificity and PPV increased (98.3% and 90%) with hardly any decrease in the sensitivity or NPV (86.3% and 97.5%). No relevant differences were observed between the three study periods. CONCLUSIONS/SIGNIFICANCE: ADA remains useful for the diagnosis of TPE even in low-to-intermediate prevalence scenarios when combined with the lymphocyte proportion