Notes about the Caratheodory number

In this paper we give sufficient conditions for a compactum in $\mathbb R^n$ to have Carath\'{e}odory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory theorem and give a Tverberg type theorem for families of convex compacta

Analogues of the central point theorem for families with dd-intersection property in Rd\mathbb R^d

In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families

Small contribution of gold mines to the ongoing tuberculosis epidemic in South Africa: a modeling-based study.

BACKGROUND: Gold mines represent a potential hotspot for Mycobacterium tuberculosis (Mtb) transmission and may be exacerbating the tuberculosis (TB) epidemic in South Africa. However, the presence of multiple factors complicates estimation of the mining contribution to the TB burden in South Africa. METHODS: We developed two models of TB in South Africa, a static risk model and an individual-based model that accounts for longer-term trends. Both models account for four populations - mine workers, peri-mining residents, labor-sending residents, and other residents of South Africa - including the size and prevalence of latent TB infection, active TB, and HIV of each population and mixing between populations. We calibrated to mine- and country-level data and used the static model to estimate force of infection (FOI) and new infections attributable to local residents in each community compared to other residents. Using the individual-based model, we simulated a counterfactual scenario to estimate the fraction of overall TB incidence in South Africa attributable to recent transmission in mines. RESULTS: We estimated that the majority of FOI in each community is attributable to local residents: 93.9% (95% confidence interval 92.4-95.1%), 91.5% (91.4-91.5%), and 94.7% (94.7-94.7%) in gold mining, peri-mining, and labor-sending communities, respectively. Assuming a higher rate of Mtb transmission in mines, 4.1% (2.6-5.8%), 5.0% (4.5-5.5%), and 9.0% (8.8-9.1%) of new infections in South Africa are attributable to gold mine workers, peri-mining residents, and labor-sending residents, respectively. Therefore, mine workers with TB disease, who constitute ~ 2.5% of the prevalent TB cases in South Africa, contribute 1.62 (1.04-2.30) times as many new infections as TB cases in South Africa on average. By modeling TB on a longer time scale, we estimate 63.0% (58.5-67.7%) of incident TB disease in gold mining communities to be attributable to recent transmission, of which 92.5% (92.1-92.9%) is attributable to local transmission. CONCLUSIONS: Gold mine workers are estimated to contribute a disproportionately large number of Mtb infections in South Africa on a per-capita basis. However, mine workers contribute only a small fraction of overall Mtb infections in South Africa. Our results suggest that curtailing transmission in mines may have limited impact at the country level, despite potentially significant impact at the mining level

How can mathematical models advance tuberculosis control in high HIV prevalence settings?

Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly

Thermal Properties and Paste and Gel Behaviors of Starches Recovered from Accessions Used in the Germplasm Enhancement of Maize Project

The objective of this study was to screen starches recovered from the corn accessions used in the Germplasm Enhancement of Maize (GEM) project for unusual thermal properties and paste and gel behaviors, so that they could be exploited in corn breeding programs to enhance traits important to corn utilization. In general, the values for gelatinization temperatures and peak height indices were greater, but heat of gelatinization values were less for the starches recovered from the GEM accessions (particularly BRA 052051 (SE 32)) than for starches from commercial Dent corn hybrids (11.3 vs. 13.6 J/g). Generally, retrogradation properties were similar among the GEM accessions, although there were specific accessions (particularly Lima 13) that possessed modestly lower percentage retrogradation (34 vs. 42%). Generally, peak viscosities, cold paste viscosities, and viscosity breakdowns were greater for the starches of the GEM accessions (particularly ARZM 01150, Antiqua 3, and URZM 01089, respectively) than for the starches of commercial hybrids. Pasting temperatures were about the same for all starches. Both 1-day and 7-day gel strengths were considerably greater for the starches recovered from the GEM accessions (particularly BRA 052051 (SE 32), 21.0 g for 1-day and FS8A(T), 66.2 g for 7-day). Although the differences in starch properties were statistically different, only the higher gel strengths of the starches recovered from the GEM accessions were of practical significance to the starch industry

Dust Explosion Propagation in Small Diameter Pipes

© 2018 American Institute of Chemical Engineers In facilities handling combustible dusts, the isolation of propagating deflagrations requires great attention due to the potential catastrophic consequences of secondary dust explosions. While the ability of dust explosions to propagate is widely recognized, some misconceptions still exist. One of the common myths is that a dust explosion cannot propagate through small diameter pipes and that explosion isolation may not be required in that case. This article first presents a simplified theory of flame propagation in pipes. Dust explosion experiments performed in industrial-scale pipes smaller or equal to 4 in (or 100 mm) in diameter are then reviewed. The findings of the experiments are interpreted in the light of the simplified theory. Our study reveals that dust explosion propagation has been consistently observed in pipes with a diameter as small as 1 in. While the likelihood of flame propagation seems to decrease with pipe diameter and other “chemical” and “engineering” factors, it remains a realistic scenario and therefore should be addressed in the design and operation of powder handling systems. © 2018 American Institute of Chemical Engineers Process Saf Prog 2018.Fik

Eliminating Malaria Vectors.

Malaria vectors which predominantly feed indoors upon humans have been locally eliminated from several settings with insecticide treated nets (ITNs), indoor residual spraying or larval source management. Recent dramatic declines of An. gambiae in east Africa with imperfect ITN coverage suggest mosquito populations can rapidly collapse when forced below realistically achievable, non-zero thresholds of density and supporting resource availability. Here we explain why insecticide-based mosquito elimination strategies are feasible, desirable and can be extended to a wider variety of species by expanding the vector control arsenal to cover a broader spectrum of the resources they need to survive. The greatest advantage of eliminating mosquitoes, rather than merely controlling them, is that this precludes local selection for behavioural or physiological resistance traits. The greatest challenges are therefore to achieve high biological coverage of targeted resources rapidly enough to prevent local emergence of resistance and to then continually exclude, monitor for and respond to re-invasion from external populations

Evaluation in Mice of a Conjugate Vaccine for Cholera Made from Vibrio cholerae O1 (Ogawa) O-Specific Polysaccharide

Background: Protective immunity against cholera is serogroup specific. Serogroup specificity in Vibrio cholerae is determined by the O-specific polysaccharide (OSP) of lipopolysaccharide (LPS). Generally, polysaccharides are poorly immunogenic, especially in young children. Methodology Here we report the evaluation in mice of a conjugate vaccine for cholera (OSP:TThc) made from V. cholerae O1 Ogawa O-Specific Polysaccharide–core (OSP) and recombinant tetanus toxoid heavy chain fragment (TThc). We immunized mice intramuscularly on days 0, 21, and 42 with OSP:TThc or OSP only, with or without dmLT, a non-toxigenic immunoadjuvant derived from heat labile toxin of Escherichia coli. Principal Findings We detected significant serum IgG antibody responses targeting OSP following a single immunization in mice receiving OSP:TThc with or without adjuvant. Anti-LPS IgG responses were detected following a second immunization in these cohorts. No anti-OSP or anti-LPS IgG responses were detected at any time in animals receiving un-conjugated OSP with or without immunoadjuvant, and in animals receiving immunoadjuvant alone. Responses were highest following immunization with adjuvant. Serum anti-OSP IgM responses were detected in mice receiving OSP:TThc with or without immunoadjuvant, and in mice receiving unconjugated OSP. Serum anti-LPS IgM and vibriocidal responses were detected in all vaccine cohorts except in mice receiving immunoadjuvant alone. No significant IgA anti-OSP or anti-LPS responses developed in any group. Administration of OSP:TThc and adjuvant also induced memory B cell responses targeting OSP and resulted in 95% protective efficacy in a mouse lethality cholera challenge model. Conclusion: We describe a protectively immunogenic cholera conjugate in mice. Development of a cholera conjugate vaccine could assist in inducing long-term protective immunity, especially in young children who respond poorly to polysaccharide antigens

Modelling the implications of stopping vector control for malaria control and elimination

Increasing coverage of malaria vector control interventions globally has led to significant reductions in disease burden. However due to its high recurrent cost, there is a need to determine if and when vector control can be safely scaled back after transmission has been reduced.; A mathematical model of Plasmodium falciparum malaria epidemiology was simulated to determine the impact of scaling back vector control on transmission and disease. A regression analysis of simulation results was conducted to derive predicted probabilities of resurgence, severity of resurgence and time to resurgence under various settings. Results indicate that, in the absence of secular changes in transmission, there are few scenarios where vector control can be removed without high expectation of resurgence. These, potentially safe, scenarios are characterized by low historic entomological inoculation rates, successful vector control programmes that achieve elimination or near elimination, and effective surveillance systems with high coverage and effective treatment of malaria cases.; Programmes and funding agencies considering scaling back or withdrawing vector control from previously malaria endemic areas need to first carefully consider current receptivity and other available interventions in a risk assessment. Surveillance for resurgence needs to be continuously conducted over a long period of time in order to ensure a rapid response should vector control be withdrawn

Vectorial capacity and vector control: reconsidering sensitivity to parameters for malaria elimination

Background: Major gains have been made in reducing malaria transmission in many parts of the world, principally by scaling-up coverage with long-lasting insecticidal nets and indoor residual spraying. Historically, choice of vector control intervention has been largely guided by a parameter sensitivity analysis of George Macdonald's theory of vectorial capacity that suggested prioritizing methods that kill adult mosquitoes. While this advice has been highly successful for transmission suppression, there is a need to revisit these arguments as policymakers in certain areas consider which combinations of interventions are required to eliminate malaria.Methods and Results: Using analytical solutions to updated equations for vectorial capacity we build on previous work to show that, while adult killing methods can be highly effective under many circumstances, other vector control methods are frequently required to fill effective coverage gaps. These can arise due to pre-existing or developing mosquito physiological and behavioral refractoriness but also due to additive changes in the relative importance of different vector species for transmission. Furthermore, the optimal combination of interventions will depend on the operational constraints and costs associated with reaching high coverage levels with each intervention.Conclusions: Reaching specific policy goals, such as elimination, in defined contexts requires increasingly non-generic advice from modelling. Our results emphasize the importance of measuring baseline epidemiology, intervention coverage, vector ecology and program operational constraints in predicting expected outcomes with different combinations of interventions.<br/