Tight hardness of the non-commutative Grothendieck problem

We prove that for any ε > 0 it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor 1=2+ε, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC’13). Our proof uses an embedding of ℓ2 into the space of matrices endowed with the trace norm with the property that the image of standard basis vectors is longer than that of unit vectors with no large coordinates. We also observe that one can obtain a tight NP-hardness result for the commutative Little Grothendieck problem; previously, this was only known based on the Unique Games Conjecture (Khot and Naor, Mathematika 2009)

Tight hardness of the non-commutative Grothendieck problem

We prove that for any $\varepsilon > 0$ it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor $1/2 + \varepsilon$, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC'13). Our proof uses an embedding of $\ell_2$ into the space of matrices endowed with the trace norm with the property that the image of standard basis vectors is longer than that of unit vectors with no large coordinates

Willingness to pay for small solar powered bed net fans: results of a Becker-DeGroot-Marschak auction in Ghana

Long-lasting insecticidal nets (LLINs) are one of the main interventions recommended by the World Health Organization for malaria vector control. LLINs are ineffective if they are not being used. Subsequent to the completion of a cluster randomized cross over trial conducted in rural Greater Accra where participants were provided with the 'Bɔkɔɔ System'-a set of solar powered net fan and light consoles with a solar panel and battery-or alternative household water filters, all trial participants were invited to participate in a Becker-DeGroot-Marschak auction to determine the mean willingness to pay (WTP) for the fan and light consoles and to estimate the demand curve for the units.; Results demonstraed a mean WTP of approximately 55 Cedis (~13 USD). Demand results suggested that at a price which would support full manufacturing cost recovery, a majority of households in the area would be willing to purchase at least one such unit

Perceptions on the effect of small electric fans on comfort inside bed nets in southern Ghana : a qualitative study

Long-lasting insecticidal nets (LLINs) are known to be highly effective in reducing malaria transmission, morbidity and mortality. However, among those owning an LLIN, use rates are often suboptimal. A reported barrier to bed net use is discomfort due to heat. This qualitative study was part of a larger evaluation conducted in communities without electricity in rural Ghana to assess whether 0.8 W solar powered net fans can increase net use.; Twenty-three key informant interviews with household heads in the study communities in Shai-Osudoku District, southern Ghana, were conducted from July to August 2015. The purpose of the interviews was to obtain insight into perceptions of participants about the net fan system in relation to LLIN use.; While all study participants reported using LLINs, with mosquito nuisance prevention as the prime motivation, heat was also mentioned as a key barrier to net use. Respondents appreciated the net fans because they improved comfort inside bed nets. The LED light on the fan stand became the main source of light at night and positively influenced the perception of the intervention as a whole.; The general acceptance of the net fan system by the study participants highlights the potential of the intervention to improve comfort inside mosquito nets. This, therefore, has a potential to increase bed net use in areas with low access to electricity

Incidence and consequences of damage to insecticide-treated mosquito nets in Kenya

BACKGROUND: Efforts to improve the impact of long-lasting insecticidal nets (LLINs) should be informed by understanding of the causes of decay in effect. Holes in LLINs have been estimated to account for 7-11% of loss in effect on vectorial capacity for Plasmodium falciparum malaria in an analysis of repeated cross-sectional surveys of LLINs in Kenya. This does not account for the effect of holes as a cause of net attrition or non-use, which cannot be measured using only cross-sectional data. There is a need for estimates of how much these indirect effects of physical damage on use and attrition contribute to decay in effectiveness of LLINs. METHODS: Use, physical integrity, and survival were assessed in a cohort of 4514 LLINs followed for up to 4 years in Kenya. Flow diagrams were used to illustrate how the status of nets, in terms of categories of use, physical integrity, and attrition, changed between surveys carried out at 6-month intervals. A compartment model defined in terms of ordinary differential equations (ODEs) was used to estimate the transition rates between the categories. Effects of physical damage to LLINs on use and attrition were quantified by simulating counterfactuals in which there was no damage. RESULTS: Allowing for the direct effect of holes, the effect on use, and the effect on attrition, 18% of the impact on vectorial capacity was estimated to be lost because of damage. The estimated median lifetime of the LLINs was 2.9 years, but this was extended to 5.7 years in the counterfactual without physical damage. Nets that were in use were more likely to be in a damaged state than unused nets but use made little direct difference to LLIN lifetimes. Damage was reported as the reason for attrition for almost half of attrited nets, but the model estimated that almost all attrited nets had suffered some damage before attrition. CONCLUSIONS: Full quantification of the effects of damage will require measurement of the supply of new nets and of household stocks of unused nets, and also of their impacts on both net use and retention. The timing of mass distribution campaigns is less important than ensuring sufficient supply. In the Kenyan setting, nets acquired damage rapidly once use began and the damage led to rapid attrition. Increasing the robustness of nets could substantially increase their lifetime and impact but the impact of LLIN programmes on malaria transmission is ultimately limited by levels of use. Longitudinal analyses of net integrity data from different settings are needed to determine the importance of physical damage to nets as a driver of attrition and non-use, and the importance of frequent use as a cause of physical damage in different contexts

Monthly entomological inoculation rate data for studying the seasoanality of malaria transmission in Africa

A comprehensive literature review was conducted to create a new database of 197 field surveys of monthly malaria Entomological Inoculation Rates (EIR), a metric of malaria transmission intensity. All field studies provide data at a monthly temporal resolution and have a duration of at least one year in order to study the seasonality of the disease. For inclusion, data collection methodologies adhered to a specific standard and the location and timing of the measurements were documented. Auxiliary information on the population and hydrological setting were also included. The database includes measurements that cover West and Central Africa and the period from 1945 to 2011, and hence facilitates analysis of interannual transmission variability over broad regions

The effect of small solar powered 'Bͻkͻͻ' net fans on mosquito net use : results from a randomized controlled cross-over trial in southern Ghana

Long-lasting insecticidal nets (LLINs) are ineffective malaria transmission prevention tools if they are unused. Discomfort due to heat is the most commonly reported reason for not using nets, but this problem is largely unaddressed. With increasing rural electrification and the dropping price of solar power, fans could improve comfort inside nets and be affordable to populations in malaria endemic areas. Here, results are presented from a pilot randomized controlled cross-over study testing the effect of fans on LLIN use.; Eighty-three households from two rural communities in Greater Accra, Ghana, randomized into three groups, participated in a 10-month cross-over trial. After a screening survey to identify eligible households, all households received new LLINs. Bͻkͻͻ net fan systems (one fan per member) were given to households in Group 1 and water filters were given to households in Group 2. At mid-point, Group 1 and 2 crossed over interventions. Households in Group 1 and 2 participated in fortnightly surveys on households' practices related to nets, fans and water filters, while households in Group 3 were surveyed only at screening, mid-point and study end. Entomological and weather data were collected throughout the study. Analysis took both 'per protocol' (PP) and 'intention to treat' (ITT) approaches. The mid- and end-point survey data from Group 1 and 2 were analysed using Firth logistic regressions. Fortnightly survey data from all groups were analysed using logistic regressions with random effects.; Provision of fans to households appeared to increase net use in this study. Although the increase in net use explained by fans was not significant in the primary analyses (ITT odds ratio 3.24, p > 0.01; PP odds ratio = 1.17, p > 0.01), it was significant in secondary PP analysis (odds ratio = 1.95, p < 0.01). Net use was high at screening and even higher after provision of new LLINs and with follow up. Fan use was 90-100% depending on the fortnightly visit.; This pilot study could not provide definitive evidence that fans increase net use. A larger study with additional statistical power is needed to assess this association across communities with diverse environmental and socio-demographic characteristics

Do Israelis understand the Hebrew bible?

The Hebrew Bible should be taught like a foreign language in Israel too, argues Ghil'ad Zuckermann, inter alia endorsing Avraham Ahuvia’s recently-launched translation of the Old Testament into what Zuckermann calls high-register 'Israeli'. According to Zuckermann, Tanakh RAM fulfills the mission of 'red 'el ha'am' not only in its Hebrew meaning (Go down to the people) but also – more importantly – in its Yiddish meaning ('red' meaning 'speak!', as opposed to its colorful communist sense). Ahuvia's translation is most useful and dignified. Given its high register, however, Zuckermann predicts that the future promises consequent translations into more colloquial forms of Israeli, a beautifully multi-layered and intricately multi-sourced language, of which to be proud.Ghil'ad Zuckerman

The Hilbertian Tensor Norm and Entangled Two-Prover Games

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.Comment: 33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6 rewritten, v3: completely rewritten in order to improve readability; title changed; references added; published versio

Mathematical Evaluation of Community Level Impact of Combining Bed Nets and Indoor Residual Spraying upon Malaria Transmission in Areas where the main Vectors are Anopheles Arabiensis Mosquitoes.

Indoor residual insecticide spraying (IRS) and long-lasting insecticide treated nets (LLINs) are commonly used together even though evidence that such combinations confer greater protection against malaria than either method alone is inconsistent. A deterministic model of mosquito life cycle processes was adapted to allow parameterization with results from experimental hut trials of various combinations of untreated nets or LLINs (Olyset, PermaNet 2.0, Icon Life nets) with IRS (pirimiphos methyl, lambda cyhalothrin, DDT), in a setting where vector populations are dominated by Anopheles arabiensis, so that community level impact upon malaria transmission at high coverage could be predicted. Intact untreated nets alone provide equivalent personal protection to all three LLINs. Relative to IRS plus untreated nets, community level protection is slightly higher when Olyset or PermaNet 2.0 nets are added onto IRS with pirimiphos methyl or lambda cyhalothrin but not DDT, and when Icon Life nets supplement any of the IRS insecticides. Adding IRS onto any net modestly enhances communal protection when pirimiphos methyl is sprayed, while spraying lambda cyhalothrin enhances protection for untreated nets but not LLINs. Addition of DDT reduces communal protection when added to LLINs. Where transmission is mediated primarily by An. arabiensis, adding IRS to high LLIN coverage provides only modest incremental benefit (e.g. when an organophosphate like pirimiphos methyl is used), but can be redundant (e.g. when a pyrethroid like lambda cyhalothin is used) or even regressive (e.g. when DDT is used for the IRS). Relative to IRS plus untreated nets, supplementing IRS with LLINs will only modestly improve community protection. Beyond the physical protection that intact nets provide, additional protection against transmission by An. arabiensis conferred by insecticides will be remarkably small, regardless of whether they are delivered as LLINs or IRS. The insecticidal action of LLINs and IRS probably already approaches their absolute limit of potential impact upon this persistent vector so personal protection of nets should be enhanced by improving the physical integrity and durability. Combining LLINs and non-pyrethroid IRS in residual transmission systems may nevertheless be justified as a means to manage insecticide resistance and prevent potential rebound of not only An. arabiensis, but also more potent, vulnerable and historically important species such as Anopheles gambiae and Anopheles funestus