In these notes, the Christoffel-Darboux polynomial kernel is extended to infinite-dimensional Hilbert spaces, following as closely as possible its original finite-dimensional treatment.
Tamara Poklar Vatovec, Zala Jenko Pražnikar, Ana Petelin
The Mediterranean diet (MD) is considered a model for good health, and is promoted worldwide as one of the healthiest dietary patterns. Despite the MD’s health benefits, the literature suggests that adherence to the MD tends to be in decline in most populations worldwide, including those in the Mediterranean region. The aim of this study was to investigate adherence to the MD, and its main sociodemographic and lifestyle factors, in the Slovenian population. Using a nationwide cross-sectional food consumption survey (SI.Menu), data were collected from a general questionnaire, from the 14-item MD adherence screener (14-MEDAS score), and from a questionnaire on the dietary habits of 850 adults and elderly people. The mean MEDAS score for the total study sample was 5.6 (SD 2.1), indicating a low adherence to the MD among the Slovenian population. The adherence to the MD was higher among women (OR = 1.534; 95% Cl 1.156–2.034), those with a university degree (OR = 1.527; 1.098–2.125; compared to those with no university degree), those who lived in a suburb or city (OR = 1.511; 1.016–2.249; OR = 1.568; 1.122–2.191; compared with those who lived in a village), non-smokers (OR = 1.561; 1.380–1.830; compared with smokers), and those who lived in the western part of Slovenia (OR = 1.558; 1.170–2.074; compared with those who lived in eastern Slovenia). Adherence to the MD in the Slovenian population is low, and is strongly related to educational level, gender, geographic region, place of residence, and smoking status. The frequency of the consumption of different food groups is also closely related.
We show that the empirical Christoffel function associated with a cloud of finitely many points sampled from a distribution, can provide a simple tool for supervised classification in data analysis, with good generalization properties.
The article provides an overview of the latest developments on control approaches for connected and automated vehicles along with their effectiveness on energy and transportation efficiency.
Abstract. Elemental carbon (EC) has been widely used as a tracer to track the portion of co-emitted primary organic carbon (OC) and, by extension, to estimate secondary OC (SOC) from ambient observations of EC and OC. Key to this EC tracer method is to determine an appropriate OC / EC ratio that represents primary combustion emission sources (i.e., (OC / EC)pri) at the observation site. The conventional approaches include regressing OC against EC within a fixed percentile of the lowest (OC / EC) ratio data (usually 5–20 %) or relying on a subset of sampling days with low photochemical activity and dominated by local emissions. The drawback of these approaches is rooted in its empirical nature, i.e., a lack of clear quantitative criteria in the selection of data subsets for the (OC / EC)pri determination. We examine here a method that derives (OC / EC)pri through calculating a hypothetical set of (OC / EC)pri and SOC followed by seeking the minimum of the coefficient of correlation (R2) between SOC and EC. The hypothetical (OC / EC)pri that generates the minimum R2(SOC,EC) then represents the actual (OC / EC)pri ratio if variations of EC and SOC are independent and (OC / EC)pri is relatively constant in the study period. This Minimum R Squared (MRS) method has a clear quantitative criterion for the (OC / EC)pri calculation. This work uses numerically simulated data to evaluate the accuracy of SOC estimation by the MRS method and to compare with two commonly used methods: minimum OC / EC (OC / ECmin) and OC / EC percentile (OC / EC10 %). Log-normally distributed EC and OC concentrations with known proportion of SOC are numerically produced through a pseudorandom number generator. Three scenarios are considered, including a single primary source, two independent primary sources, and two correlated primary sources. The MRS method consistently yields the most accurate SOC estimation. Unbiased SOC estimation by OC / ECmin and OC / EC10 % only occurs when the left tail of OC / EC distribution is aligned with the peak of the (OC / EC)pri distribution, which is fortuitous rather than norm. In contrast, MRS provides an unbiased SOC estimation when measurement uncertainty is small. MRS results are sensitive to the magnitude of measurement uncertainty but the bias would not exceed 23 % if the uncertainty is within 20 %.
We show that there is no general algorithm which finds a sequence of points with finite-precision converging computably to the global optima of any continuous function.
In this paper we prove the existence and uniqueness theorem, comparison theorem of a class of anticipated mean-field backward stochastic differential equations with jumps.
In this paper we solve the Monge problem on infinite dimensional Hilbert space endowed with a suitable Gaussian measure, that satisfies the Lebesgue differentiation theorem.
We provide a full self-contained proof of a famous Lemma of Ilmanen. This proof is based on a regularisation procedure similar to Lasry-Lions regularisation.
In an infinite-horizon optimal control problem the stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.