Nearly Optimal Bounds for Sample-Based Testing and Learning of kk-Monotone Functions

We study monotonicity testing of functions $f \colon \{0,1\}^d \to \{0,1\}$ using sample-based algorithms, which are only allowed to observe the value of $f$ on points drawn independently from the uniform distribution. A classic result by Bshouty-Tamon (J. ACM 1996) proved that monotone functions can be learned with $\exp(O(\min\{\frac{1}{\varepsilon}\sqrt{d},d\}))$ samples and it is not hard to show that this bound extends to testing. Prior to our work the only lower bound for this problem was $\Omega(\sqrt{\exp(d)/\varepsilon})$ in the small $\varepsilon$ parameter regime, when $\varepsilon = O(d^{-3/2})$, due to Goldreich-Goldwasser-Lehman-Ron-Samorodnitsky (Combinatorica 2000). Thus, the sample complexity of monotonicity testing was wide open for $\varepsilon \gg d^{-3/2}$. We resolve this question, obtaining a tight lower bound of $\exp(\Omega(\min\{\frac{1}{\varepsilon}\sqrt{d},d\}))$ for all $\varepsilon$ at most a sufficiently small constant. In fact, we prove a much more general result, showing that the sample complexity of $k$-monotonicity testing and learning for functions $f \colon \{0,1\}^d \to [r]$ is $\exp(\Theta(\min\{\frac{rk}{\varepsilon}\sqrt{d},d\}))$. For testing with one-sided error we show that the sample complexity is $\exp(\Theta(d))$. Beyond the hypercube, we prove nearly tight bounds (up to polylog factors of $d,k,r,1/\varepsilon$ in the exponent) of $\exp(\widetilde{\Theta}(\min\{\frac{rk}{\varepsilon}\sqrt{d},d\}))$ on the sample complexity of testing and learning measurable $k$-monotone functions $f \colon \mathbb{R}^d \to [r]$ under product distributions. Our upper bound improves upon the previous bound of $\exp(\widetilde{O}(\min\{\frac{k}{\varepsilon^2}\sqrt{d},d\}))$ by Harms-Yoshida (ICALP 2022) for Boolean functions ($r=2$)

Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing

We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions f:{0,1}^d ? ?. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function f over an arbitrary partially ordered domain as a collection of Boolean functions over the same domain, roughly capturing the distance of f to monotonicity and the structure of violations of f to monotonicity. We apply our generalized isoperimetric inequality to improve algorithms for testing monotonicity and approximating the distance to monotonicity for real-valued functions. Our tester for monotonicity has query complexity O?(min(r ?d,d)), where r is the size of the image of the input function. (The best previously known tester makes O(d) queries, as shown by Chakrabarty and Seshadhri (STOC 2013).) Our tester is nonadaptive and has 1-sided error. We prove a matching lower bound for nonadaptive, 1-sided error testers for monotonicity. We also show that the distance to monotonicity of real-valued functions that are ?-far from monotone can be approximated nonadaptively within a factor of O(?{d log d}) with query complexity polynomial in 1/? and the dimension d. This query complexity is known to be nearly optimal for nonadaptive algorithms even for the special case of Boolean functions. (The best previously known distance approximation algorithm for real-valued functions, by Fattal and Ron (TALG 2010) achieves O(d log r)-approximation.

Evolutionary biology and anthropology suggest biome reconstitution as a necessary approach toward dealing with immune disorders

Industrialized society currently faces a wide range of non-infectious, immune-related pandemics. These pandemics include a variety of autoimmune, inflammatory and allergic diseases that are often associated with common environmental triggers and with genetic predisposition, but that do not occur in developing societies. In this review, we briefly present the idea that these pandemics are due to a limited number of evolutionary mismatches, the most damaging being ‘biome depletion’. This particular mismatch involves the loss of species from the ecosystem of the human body, the human biome, many of which have traditionally been classified as parasites, although some may actually be commensal or even mutualistic. This view, evolved from the ‘hygiene hypothesis’, encompasses a broad ecological and evolutionary perspective that considers host-symbiont relations as plastic, changing through ecological space and evolutionary time. Fortunately, this perspective provides a blueprint, termed 'biome reconstitution', for disease treatment and especially for disease prevention. Biome reconstitution includes the controlled and population-wide reintroduction (i.e. domestication) of selected species that have been all but eradicated from the human biome in industrialized society and holds great promise for the elimination of pandemics of allergic, inflammatory and autoimmune diseases

Cocoa plant productivity in West Africa under climate change: a modelling and experimental study

The potential effect of climate change on regional suitability for cocoa cultivation is a serious economic concern for West Africa - especially for Ghana and Côte d’Ivoire, whose cocoa cultivation accounts for respectively ~19% and ~45% of world production. Here, we present a modelling and observational study of cocoa net primary productivity (NPP) in present day and future West African climates. Our analysis uses a data assimilation technique to parameterise a process-based land-surface model. The parameterisation is based on laboratory observations of cocoa, grown under both ambient and elevated CO . Present day and end of 21st century cocoa 2 cultivation scenarios are produced by driving the parameterised land-surface model with output from a high-resolution climate model. This represents a significant advance on previous work, because unlike the CMIP5 models, the high-resolution model used in this study accurately captures the observed precipitation seasonality in the cocoa-growing regions of West Africa - a key sensitivity for perennials like cocoa. We find that temperature is projected to increase significantly and precipitation is projected to increase slightly, although not in all parts of the region of interest. We find, furthermore, that the physiological effect of higher atmospheric CO2 concentration ameliorates the impacts of high temperature and variation in precipitation thereby reducing some of the negative impacts of climate change and maintaining net primary productivity in West Africa, for the whole 21st Century, even under a high emissions scenario. Although NPP is an indicator of general vegetation condition, it is not equivalent to yield or bean quality. The study presented here is, nevertheless, a strong basis for further field and modelling studies of cultivation under elevated CO2 conditions

Assessment of the proportion of neonates and children in low and middle income countries with access to a healthcare facility: A systematic review

<p>Abstract</p> <p>Background</p> <p>Comprehensive antenatal, perinatal and early postnatal care has the potential to significantly reduce the 3.58 million neonatal deaths that occur annually worldwide. This paper systematically reviews data on the proportion of neonates and children < 5 years of age that have access to health facilities in low and middle income countries. Gaps in available data by WHO region are identified, and an agenda for future research and advocacy is proposed.</p> <p>Methods</p> <p>For this paper, "utilization" was used as a proxy for "access" to a healthcare facility, and the term "facility" was used for any clinic or hospital outside of a person's home staffed by a "medical professional". A systematic literature search was conducted for published studies of children up to 5 years of age that included the neonatal age group with an illness or illness symptoms in which health facility utilization was quantified. In addition, information from available Demographic and Health Surveys (DHS) was extracted.</p> <p>Results</p> <p>The initial broad search yielded 2,239 articles, of which 14 presented relevant data. From the community-based neonatal studies conducted in the Southeast Asia region with the goal of enhancing care-seeking for neonates with sepsis, the 10-48% of sick neonates in the studies' control arms utilized a healthcare facility. Data from cross-sectional surveys involving young children indicate that 12 to 86% utilizing healthcare facilities when sick. From the DHS surveys, a global median of 58.1% of infants < 6 months were taken to a facility for symptoms of ARI.</p> <p>Conclusions</p> <p>There is a scarcity of data regarding the access to facility-based care for sick neonates/young children in many areas of the world; it was not possible to generalize an overall number of neonates or young children that utilize a healthcare facility when showing signs and symptoms of illness. The estimate ranges were broad, and there was a paucity of data from some regions. It is imperative that researchers, advocates, and policy makers join together to better understand the factors affecting health care utilization/access for newborns in different settings and what the barriers are that prevent children from being taken to a facility in a timely manner.</p

Care Seeking for Neonatal Illness in Low- and Middle-Income Countries: A Systematic Review

Hadley Herbert and colleagues systematically review newborn care-seeking behaviors by caregivers in low- and middle-income countries

Writing in Britain and Ireland, c. 400 to c. 800

No abstract available

Measurement of the p-pbar -> Wgamma + X cross section at sqrt(s) = 1.96 TeV and WWgamma anomalous coupling limits

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.Comment: Submitted to Phys. Rev. D Rapid Communication