Helly-Type Theorems in Property Testing

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into $k$ clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object $G$. In this paper, as an application of Helly's theorem, by taking a constant size sample from $S$, we present a testing algorithm for $(k,G)$-clustering, i.e., to distinguish between two cases: when $S$ is $(k,G)$-clusterable, and when it is $\epsilon$-far from being $(k,G)$-clusterable. A set $S$ is $\epsilon$-far $(0<\epsilon\leq1)$ from being $(k,G)$-clusterable if at least $\epsilon n$ points need to be removed from $S$ to make it $(k,G)$-clusterable. We solve this problem for $k=1$ and when $G$ is a symmetric convex object. For $k>1$, we solve a weaker version of this problem. Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Multi sensor transducer and weight factor

A multi-sensor transducer and processing method allow insitu monitoring of the senor accuracy and transducer `health`. In one embodiment, the transducer has multiple sensors to provide corresponding output signals in response to a stimulus, such as pressure. A processor applies individual weight factors to reach of the output signals and provide a single transducer output that reduces the contribution from inaccurate sensors. The weight factors can be updated and stored. The processor can use the weight factors to provide a `health` of the transducer based upon the number of accurate versus in-accurate sensors in the transducer

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Modelling the impact of social protection on tuberculosis: the S-PROTECT project.

BACKGROUND: Tackling the social determinants of Tuberculosis (TB) through social protection is a key element of the post-2015 End TB Strategy. However, evidence informing policies are still scarce. Mathematical modelling has the potential to contribute to fill this knowledge gap, but existing models are inadequate. The S-PROTECT consortium aimed to develop an innovative mathematical modelling approach to better understand the role of social protection to improve TB care, prevention and control. METHODS: S-PROTECT used a three-steps approach: 1) the development of a conceptual framework; 2) the extraction from this framework of three high-priority mechanistic pathways amenable for modelling; 3) the development of a revised version of a standard TB transmission model able to capture the structure of these pathways. As a test case we used the Bolsa Familia Programme (BFP), the Brazilian conditional cash transfer scheme. RESULTS: Assessing one of these pathways, we estimated that BFP can reduce TB prevalence by 4% by improving households income and thus their nutritional status. When looking at the direct impact via malnutrition (not income mediated) the impact was 33%. This variation was due to limited data availability, uncertainties on data transformation and the pathway approach taken. These results are preliminary and only aim to serve as illustrative example of the methodological challenges encountered in this first modelling attempt, nonetheless they suggest the potential added value of integrating TB standard of care with social protection strategies. CONCLUSIONS: Results are to be confirmed with further analysis. However, by developing a generalizable modelling framework, S-PROTECT proved that the modelling of social protection is complex, but doable and allowed to draw the research road map for the future in this field

Thermal ageing phenomena and strategies towards reactivation of NO x - storage catalysts

The thermal ageing and reactivation of Ba/CeO2 and Ba/Al2O3 based NO x -storage/ reduction (NSR) catalysts was studied on model catalysts and catalyst systems at the engine. The mixed oxides BaAl2O4 and BaCeO3, which lower the storage activity, are formed during ageing above 850°C and 900°C, respectively. Interestingly, the decomposition of BaCeO3 in an atmosphere containing H2O/NO2 leads again to NO x -storage active species, as evidenced by comparison of fresh, aged and reactivated Pt-Ba/CeO2 based model catalysts. This can be technically exploited, particularly for the Ba/CeO2 catalysts, as reactivation studies on thermally aged Ba/CeO2 and Ba/Al2O3 based NSR catalysts on an engine bench showed. An on-board reactivation procedure is presented, that improved the performance of a thermally aged catalyst significantl

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

Advantages and Limitations of Commercially Available Electrocuting Grids for Studying Mosquito Behaviour.

Mosquito feeding behaviour plays a major role in determining malaria transmission intensity and the impact of specific prevention measures. Human Landing Catch (HLC) is currently the only method that can directly and consistently measure the biting rates of anthropophagic mosquitoes, both indoors and outdoors. However, this method exposes the participant to mosquito-borne pathogens, therefore new exposure-free methods are needed to replace it. Commercially available electrocuting grids (EGs) were evaluated as an alternative to HLC using a Latin Square experimental design in Dar es Salaam, Tanzania. Both HLC and EGs were used to estimate the proportion of human exposure to mosquitoes occurring indoors (πi), as well as its two underlying parameters: the proportion of mosquitoes caught indoors (Pi) and the proportion of mosquitoes caught between the first and last hour when most people are indoors (Pfl). HLC and EGs methods accounted for 69% and 31% of the total number of female mosquitoes caught respectively and both methods caught more mosquitoes outdoors than indoors. Results from the gold standard HLC suggest that An. gambiae s.s. in Dar es Salaam is neither exophagic nor endophagic (Pi ≈ 0.5), whereas An. arabiensis is exophagic (Pi < < 0.5). Both species prefer to feed after 10 pm when most people are indoors (Pfl > >0.5). EGs yielded estimates of Pi for An. gambiae s.s., An. arabiensis and An. coustani, that were approximately equivalent to those with HLC but significantly underestimated Pfl for An. gambiae s.s. and An. coustani. The relative sampling sensitivity of EGs declined over the course of the night (p ≤ 0.001) for all mosquito taxa except An. arabiensis. Commercial EGs sample human-seeking mosquitoes with high sensitivity both indoors and outdoors and accurately measure the propensity of Anopheles malaria vectors to bite indoors rather than outdoors. However, further modifications are needed to stabilize sampling sensitivity over a full nocturnal cycle so that they can be used to survey patterns of human exposure to mosquitoes

Fine material in grain

Fine material in grain: an overview / Richard Stroshine -- Factors that affect the costs of fines in the corn export market / Lowell D. Hill, Mack Leath -- Effects of fine material on mold growth in grain / David B. Sauer, Richard A. Meronuck, John Tuite -- Effects of fine material on insect infestation: a review / Paul W. Flinn, William H. McGaughey, Wendell E. Burkholder -- Reducing or controlling damage to grain from handling: a review / Charles R. Martin, George H. Foster -- Evaluating grain for potential production of fine material - breakage susceptibility testing / Steven R. Eckhoff -- Genotypic differences in breakage susceptibility of corn and soybeans -- M. R. Paulsen, L. L. Darrah, R. L. Stroshin

Entomological Surveillance of Behavioural Resilience and Resistance in Residual Malaria Vector Populations.

The most potent malaria vectors rely heavily upon human blood so they are vulnerable to attack with insecticide-treated nets (ITNs) and indoor residual spraying (IRS) within houses. Mosquito taxa that can avoid feeding or resting indoors, or by obtaining blood from animals, mediate a growing proportion of the dwindling transmission that persists as ITNs and IRS are scaled up. Increasing frequency of behavioural evasion traits within persisting residual vector systems usually reflect the successful suppression of the most potent and vulnerable vector taxa by IRS or ITNs, rather than their failure. Many of the commonly observed changes in mosquito behavioural patterns following intervention scale-up may well be explained by modified taxonomic composition and expression of phenotypically plastic behavioural preferences, rather than altered innate preferences of individuals or populations. Detailed review of the contemporary evidence base does not yet provide any clear-cut example of true behavioural resistance and is, therefore, consistent with the hypothesis presented. Caution should be exercised before over-interpreting most existing reports of increased frequency of behavioural traits which enable mosquitoes to evade fatal contact with insecticides: this may simply be the result of suppressing the most behaviourally vulnerable of the vector taxa that constituted the original transmission system. Mosquito taxa which have always exhibited such evasive traits may be more accurately described as behaviourally resilient, rather than resistant. Ongoing national or regional entomological monitoring surveys of physiological susceptibility to insecticides should be supplemented with biologically and epidemiologically meaningfully estimates of malaria vector population dynamics and the behavioural phenotypes that determine intervention impact, in order to design, select, evaluate and optimize the implementation of vector control measures