We study metric properties of sets which are characterized by their approximation properties by smooth curves at scales of positive density and their relationships with known problems in complex dynamics and analysis. Three direct applications towards removability for bounded analytic functions, optimal bounds for Traveling Salesman problem, and Hausdorff dimension of unfolding attractors are discussed in the paper. The main technical ingredient is a construction, for every continuum K, of a finite Radon measure of bounded Menger curvature such that on every ball B(x, r), x is an element of K, the measure is bounded by a universal constant multiple of r exp(-g(x, r)), where g(x, r) >= 0 is an explicit function. Theorem A is the main analytical result of the paper and provides a precise estimate on the growth of the function g(x, r) in terms of Jones' beta numbers. Its dimension theory counterpart is stated as Theorems 1 and 2 and yields sharp estimates of the Hausdorff dimension of compacta in terms of asymptotic properties of log g(x, r)/ log r for all x is an element of K except for a set of finite linear measure. (C) 2022 Elsevier Inc. All rights reserved.

In this paper we present a theoretical foundation for a representation of a data set as a measure in a very large hierarchically parametrized family of positive measures, whose parameters can be computed explicitly (rather than estimated by optimization), and illustrate its applicability to a wide range of data types. The pre-processing step then consists of representing data sets as simple measures. The theoretical foundation consists of a dyadic product formula representation lemma, a visualization theorem. We also define an additive multiscale noise model which can be used to sample from dyadic measures and a more general multiplicative multiscale noise model which can be used to perturb continuous functions, Borel measures, and dyadic measures. The first two results are based on theorems. The representation uses the very simple concept of a dyadic tree, and hence is widely applicable, easily understood, and easily computed. Since the data sample is represented as a measure, subsequent analysis can exploit statistical and measure theoretic concepts and theories. Because the representation uses the very simple concept of a dyadic tree defined on the universe of a data set and the parameters are simply and explicitly computable and easily interpretable and visualizable, we hope that this approach will be broadly useful to mathematicians, statisticians, and computer scientists who are intrigued by or involved in data science including its mathematical foundations.

It has been empirically observed that eigenfunctions of Laplace's equation -Delta phi = lambda phi with Neumann boundary conditions sometimes localize near the boundary of the domain if that boundary is rough (say, fractal). This has some nontrivial implications in acoustics that has been put to real-life use (sound attenuation by noise-protective walls); this short paper describes the mathematical mechanism responsible for this and describes the quantitative strength of the phenomenon for some examples.

Potatoes grown in soil with high Cd concentrations can accumulate high levels of Cd in the tubers. Although there is significant environmental variation involved in the trait of crop uptake of Cd, there are also distinctive cultivar differences. In order to understand this differential Cd accumulation mechanism, two potato cultivars were chosen that accumulate high and low levels of Cd in tubers. The patterns of Cd concentration, Cd content and dry weight accumulation of the two cultivars were examined at different stages of plant growth. The data suggest that differences in total Cd uptake and in Cd partitioning among organs are the mechanisms governing differential Cd-tuber accumulation in the two cultivars. The low tuber-Cd accumulator exhibited lower root-to-shoot and shoot-to-tuber translocation driven by higher root and shoot biomass that retained more Cd in roots and shoots, respectively, reducing its movement to the tubers. Higher remobilization and more efficient tuber loading was observed in the high tuber-Cd accumulator, indicating that remobilization of Cd from leaves to tubers was a major factor, not only in tuber-Cd loading, but also in the establishment of differential tuber-Cd levels. Regardless of cultivar differences, the concentration of Cd in the tuber was very low compared to that in other organs suggesting that, despite its high phloem mobility, Cd tends to be sequestered in the shoots.

The effects of interspecific competition between the potato cyst nematodes (PCN), Globodera pallida and G. rostochiensis, under variable population conditions were examined. PCN-susceptible potato cultivars were inoculated with single-and mixed-species populations of PCN. There was a significant difference in species multiplication between single-and mixed-species populations. Globodera rostochiensis multiplication in mixed-species populations was significantly lower than single-species populations. Density-dependent trials showed a significantly greater increase in multiplication of G. pallida at low inoculation densities relative to G. rostochiensis. These results indicate that G. pallida has a negative effect on G. rostochiensis populations and is the more successful species when competing. A staggered inoculation trial showed that the greater competitiveness of G. pallida was not wholly attributed to its later hatch. Globodera pallida outcompeted G. rostochiensis regardless of the timing of inoculation; however, G. pallida multiplication was lowest when plants were simultaneously inoculated with both species.

We develop a method for classification of works of art based on their price dynamics. The method is in the same spirit as factor models commonly used within financial economics. Factor models assume that price dynamics of assets are related to underlying fundamental characteristics. We assume that such characteristics exist for works of art, and that they are associated with what we intuitively think of as style. We use a clustering algorithm to group artists that represent similar styles. This algorithm is specifically well-suited for situations where statistical distributions are far from normal – a description we believe fits well with markets for art. We test the method empirically on a ten-year sample of price data for paintings by 58 artists. Even with this limited data set, we clearly identify five groups and show that these are related to a standard classification of style.

Soil samples taken from the ridge of field-grown potato (cv. British Queen) as well as from bulk soil of the same field were incubated with sterile potato root leachate or water. Samples were filtered and filtrates used in an in vitro bioassay to determine their effect on hatch of potato cyst nematodes (PCN) Globodera rostochiensis and G. pallida. Concurrently, an experiment was established where the sterile potato root leachate or water was incubated with a sterile soil wash. Ridge soil was shown to induce significantly more hatching than bulk soil, indicating the presence of PCN hatching factors. When a soil wash of ridge soil was used it did not increase hatch, suggesting a role for soil microorganisms in the hatching process. Greater hatch of G. rostochiensis in bulk soil compared to G. pallida suggests a role for soil microorganisms in spontaneous hatch of PCN in vivo.

We revise the Levy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based 'geometrical features' at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains.

Three bacterial isolates, SB13 (Acinetobacter sp.), SB14 (Arthrobacter sp.) and SB15 (Bacillus sp.), were previously isolated from the rhizosphere of sugar beet (Beta vulgaris ssp. vulgaris) plants and shown to increase hatch of potato cyst nematodes in vitro. In this study, the three isolates were assayed for rhizosphere competence. Each isolate was applied to seeds at each of four concentrations (105-108 CFU ml−1) and the inoculated seeds were planted in plastic microcosms containing coarse sand. All three isolates were shown to colonise the rhizosphere, although to differing degrees, with the higher inoculation densities providing significantly better colonisation. The isolates increased sugar beet root and shoot dry weight. Isolates SB14 and SB15 were analysed for their ability to induce in vivo hatch of Globodera pallida in non-sterile soil planted with sugar beet. After 4 and 6 weeks, both isolates had induced significantly greater percentage hatch compared to controls.

BACKGROUNDHow multimorbidity and socio-economic factors influence healthcare costs is unknown. Geo-demographic profiling system, Mosaic, which adds to socio-economic factors, provides the potential for an investigation of the relationship with multimorbidity, and their influence on healthcare costs.METHODSUsing chronic obstructive pulmonary disease (COPD) and chronic heart failure (CHF) registers from 53 general practices for a population aged 40 years and over in Stoke-on-Trent, England (N = 10,113), were linked to hospital admissions data and Healthcare Resource Groups as a measure of hospital cost (2007-09). Eleven Mosaic groups were linked on the basis of individual patients' post codes.RESULTSThe COPD and CHF multimorbid group (n = 763) had the highest proportion with at least one hospital admission in the 3-year time period (n = 550, 72%), compared with the index COPD (56%) and CHF (66%) groups. Multimorbid patients had significantly higher mean costs for hospital admission (£4896) compared with the index COPD (£2769) or CHF (£3876). The associations between multimorbid groups and hospital admission costs compared with index groups varied by different Mosaic groups.CONCLUSIONSCHF and COPD multimorbidity is associated with high costs, and average hospital admission costs vary by Mosaic segmentation. Multimorbidity and Mosaic provide an innovative basis for developing and targeting healthcare interventions in high-hospital-cost patients.

AIM:Evidence suggests that folic acid intake affects birth weight and that these effects may be mediated via the fetal epigenome. Our previous array data indicate that methylation in human cord blood at gene-specific CpGs is associated with birth weight percentile (BWP). Our aims were to investigate associations with BWP in specific CpGs identified by the array analysis in a significantly larger cohort and investigate the effects of other relevant factors on this association. MATERIALS & METHODS:Methylation status was examined in candidate CpGs in 129 cord blood samples using Pyrosequencing™. The effects of other potentially important factors; maternal smoking, folate-related metabolite levels and genetic variation in the MTHFR gene, were examined. Linear and logistic regression analyses were used to identify relationships between BWP and methylation levels in the context of other key factors. RESULTS:Increased cord methylation at CpGs in GSTM5 and MAP2K3 was associated with a reduced risk of having a birth weight below the 50th percentile (p = 0.010; odds ratio [OR]: 0.33 and p = 0.024; OR: 0.24, respectively) while higher methylation levels in APOB were associated with an increased risk (p = 0.023; OR: 2.56). Smoking during pregnancy modified the effect of methylation on BWP. Thus, compared with nonsmokers with a GSTM5 methylation level of >25% (median BWP: 54.7%), those who had smoked during pregnancy and whose GSTM5 methylation was <25% had the lowest median BWP (12.0%; p = 0.001). Furthermore, this latter group had the highest proportion of cases with BWPs below 50% (92.9 compared with 47.8% in nonsmokers with a GSTM5 methylation level of >25%; p = 0.013; OR: 14.2). Similar results were identified for MAP2K3, while the link with APOB reflected the inverse relationship between methylation at this locus and BWP. CONCLUSION:Our data suggest that gene-specific methylation of cord DNA is associated with BWP and this methylation provides an additional effect on BWP to that of smoking during pregnancy.

Objective To investigate multimorbidity transitions from general practice populations across healthcare interfaces and the associated healthcare costs.Design Clinical-linkage database study.Setting Population (N=60660) aged 40years and over registered with 53 general practices in Stoke-on-Trent.Participants Population with six specified multimorbidity pairs were identified based on hypertension, diabetes mellitus (DM), coronary heart disease (CHD), chronic obstructive pulmonary disease (COPD), congestive heart failure (CHF) and chronic kidney disease (CKD).Main outcomes measures Chronic disease registers were linked to accident and emergency (A&E) and hospital admissions for a 3-year time period (2007-2009), and associated costs measured by Healthcare Resource Groups. Associations between multimorbid groups and direct healthcare costs were compared with their respective single disease groups using linear regression methods, adjusting for age, gender and deprivation.Results In the study population, there were 9735 patients with hypertension and diabetes (16%), 3574 with diabetes and CHD (6%), 2894 with diabetes and CKD (5%), 1855 with COPD and CHD (3%), 754 with CHF and COPD (1%) and 1425 with CHF and CKD (2%). Transition, defined as at least one episode in each of the 3-year time periods, was as follows: patients with hypertension and DM had the fewest transitions in the 3-year time period (37% A&E episode and 51% hospital admission), but those with CHF and CKD had the most transitions (67% A&E episode and 79% hospital admission). The average 3-year total costs per multimorbid patient for A&E episodes ranged from 69 to 166 pound and for hospital admissions ranged from between 2289 pound and 5344 pound. The adjusted costs were significantly higher for all six multimorbid groups compared with their respective single disease groups.Conclusions Specific common multimorbid pairs are associated with higher healthcare transitions and differential costs. Identification of multimorbidity type and linkage of information across interfaces provides opportunities for targeted intervention and delivery of integrated care.

We present a randomized algorithm for the approximate nearest neighbor problem in d -dimensional Euclidean space. Given N points { x j } in , the algorithm attempts to find k nearest neighbors for each of x j , where k is a user-specified integer parameter. The algorithm is iterative, and its running time requirements are proportional to T · N ·( d ·(log d ) + k ·( d + log k )·(log N )) + N · k 2 ·( d + log k ), with T the number of iterations performed. The memory requirements of the procedure are of the order N ·( d + k ). A by-product of the scheme is a data structure, permitting a rapid search for the k nearest neighbors among { x j } for an arbitrary point . The cost of each such query is proportional to T ·( d ·(log d ) + log( N / k )· k ·( d + log k )), and the memory requirements for the requisite data structure are of the order N ·( d + k ) + T ·( d + N ). The algorithm utilizes random rotations and a basic divide-and-conquer scheme, followed by a local graph search. We analyze the scheme’s behavior for certain types of distributions of { x j } and illustrate its performance via several numerical examples.

BACKGROUND:Non-steroidal anti-inflammatory drugs (NSAIDs) are widely regarded as one risk factor, which influences chronic kidney disease (CKD) progression. However, previous literature reviews have not quantified the risk in moderate to severe CKD patients. OBJECTIVE:To estimate the strength of association between chronic NSAID use and CKD progression. METHODS:We conducted a systematic review and meta-analysis of observational general practice or population studies featuring patients aged 45 years and over. The electronic databases searched were MEDLINE, EMBASE, Cochrane, AMED, BNI and CINAHL until September 2011 without date or language restrictions. Searches included the reference lists of relevant identified studies, WEB of KNOWLEDGE, openSIGLE, specific journals, the British Library and expert networks. For relevant studies, random effects meta-analysis was used to estimate the association between NSAID use and accelerated CKD progression (estimated glomerular filtration rate decline ≥ 15 ml/min/1.73 m2). RESULTS:From a possible 768 articles, after screening and selection, seven studies were identified (5 cohort, 1 case-control and 1 cross-sectional) and three were included in the meta-analysis. Regular-dose NSAID use did not significantly affect the risk of accelerated CKD progression; pooled odds ratio (OR) = 0.96 (95%CI: 0.86-1.07), but high-dose NSAID use significantly increased the risk of accelerated CKD progression; pooled OR = 1.26 (95%CI: 1.06-1.50). CONCLUSIONS:The avoidance of NSAIDs in the medium term is unnecessary in patients with moderate to severe CKD, if not otherwise contraindicated. As the definition of high-dose of NSAID use remains unclear, the lowest effective dose of NSAIDs should be prescribed where indicated.

We study lower and upper bounds of the Hausdorff dimension for sets which are wiggly at scales of positive density. The main tech- nical ingredient is a construction, for every continuum K, of a Borel probabilistic measure μ with the property that on every ball B(x,r), x ∈ K, the measure is bounded by a universal constant multiple of r exp(−g(x, r)), where g(x, r) ≥ 0 is an explicit function. The continuum K is mean wiggly at exactly those points x ∈ K where g(x,r) has a logarithmic growth to ∞ as r→0. The theory of mean wiggly continua leads, via the product formula for dimensions, to new esti- mates of the Hausdorff dimension for Cantor sets. We prove also that asymptotically flat sets are of Hausdorff dimension 1 and that asymp- totically non-porous continua are of the maximal dimension. Another application of the theory is geometric Bowen's dichotomy for Topolog- ical Collet-Eckmann maps in rational dynamics. In particular, mean wiggly continua are dynamically natural as they occur as Julia sets of quadratic polynomials for parameters from a generic set on the bound- ary of the Mandelbrot set M.

Six potato (Solanum tuberosum) cultivars (Home Guard, Bintje, British Queen, Mans Piper, Pentland Dell and Saturna) were inoculated with Vaminoc (a commercial mixture of three selected arbuscular mycorrhizal fungal (AMF) isolates) and with two of the individual AMF isolates present in Vaminoc, Glomus intraradices (BioRize BB-E) and Glomus mosseae (isolate BEG 12). Root length colonisation by AMF at 6 weeks after shoot emergence ranged from 49 to 54%, with Vaminoc exhibiting the highest percentage. In comparison with control plants, AMF-inoculated plants accelerated the in vitro hatch (21% mean increase) of the potato cyst nematode (PCN) species Globodera pallida (but not of G. rostochiensis) in potato root leachate collected 3 weeks after shoot emergence. The effects of mycorrhization on PCN hatch were broadly similar across the six potato cultivars. This consistency supports the potential use of AMF inoculation of potato plants as part of an integrated pest management strategy for G. pallida.

This paper is devoted to the decomposition of an image f into u + v, with u a piecewise-smooth or "cartoon" component, and v an oscillatory component (texture or noise), in a variational approach. The cartoon component u is modeled by a function of bounded variation, while v, usually represented by a square integrable function, is now being modeled by a more refined and weaker texture norm, as a distribution. Generalizing the idea of Y. Meyer [34], where v is an element of F = div(BMO) = B(M) over dotO(-1), we model here the texture component by the action of the Riesz potentials on v that belongs to BMO or to L-p. In an earlier work [28], the authors proposed energy minimization models to approximate (BV, F) decompositions explicitely expressing the texture as divergence of vector fields in BMO. In this paper, we consider an equivalent more isotropic norm of the space F in terms of the Riesz potentials, and study models where the Riesz potentials of oscillatory components belong to BMO or to L-p, 1 <= p < infinity (thus we consider oscillatory components in B(M) over dotO(alpha) or in (W) over dot(alpha,p), with alpha < 0). Theoretical, experimental results and comparisons to validate the proposed methods are presented.

H Han, Bin, 228 Hangelbroek, Thomas, 169 J Jia, Rong-Qing, 444 Jiang, Qingtang, 370 Jones, Peter W., 392 K Kähler, Uwe, 325 Khazanovsky, Marie, 98 Kong, Wai Yip, 346 Krivoshein, A., 410 L Laska, Jason N., 429 Leblond, Juliette, 264 Li, Song, 249, 460 M Mo, Qun, 249, 460 N Needell, Deanna, 59 Nguyen, Ha Q., 74 O Ólafsson, Gestur, 303 P Partington, Jonathan R., 264 Pérez-Romero, E., 143 Pounds, Dale K., 370 … R Randall, Paige, 59 Rokhlin, Vladimir, 346 S Schmid, Dominik, 169 Shen, Zuowei, 185, 228 Shi, Lei, 286 Shubov, Marianna A., 125 Šikic, Hrvoje, 26 Sincich, Eva, 264 Singer, Amit, 44 Skopina, M., 410 T Teschke, Gerd, 325 V Varshney, Lav R., 74 W Wilson, Edward N., 26 Wu, Hau-tieng, 44 Y Ye, Gui-Bo, 185 Z Zayed, Ahmed I., 125 Zhang, H., 454 Zhang, Haizhang, 1 Zhang, Jun, 1 Zheludev, Valery A., 98 Zhou, Ding-Xuan, 286 Zhu, W., 454