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The establishment of a reference method for the determination of the allergen protein content in a processed food material has been explored. An analytical approach was developed to enable the comparability of food allergen measurement results expressed in a decision-relevant manner. A proof of concept is here presented, resulting in quantity values for the common measurand, namely ‘mass of total allergen protein per mass of food’. The quantities are determined with SI traceability to enable the comparability of reported results. A method for the quantification of total milk protein content in an incurred baked food at a concentration level clinically relevant is presented. The strategy on how to obtain the final analytical result is outlined. Challenges associated with this method are discussed, in particular the optimal extraction of the marker proteins, the complete digestion and release of the peptides in an equimolar fashion, the use of conversion factors to translate the amount of measured proteins into total milk protein and the estimation of the uncertainty contributions as well as of the combined uncertainty of the final result. The implementation of such a reference method for the determination of the total allergen content in a processed food is an important step, which will provide comparable measurement data of relevance to risk assessors. Graphical abstract Electronic supplementary material The online version of this article (10.1007/s00216-020-02959-0) contains supplementary material, which is available to authorized users.

In this note, we point out several gaps in Gurudwan and Sharma (Appl. Math. Comput. 217(15):6748-6754, 2011) and Yang (Appl. Math. Comput. 218(21):10367-10369, 2012) and give the main results under weaker conditions. MSC: 47H10; 47H09; 46B20

A symmetric matrix of order n is called completely positive if it has a symmetric factorization by means of a rectangular matrix with n columns and no negative entries (a so-called cp factorization), i.e., if it can be interpreted as a Gram matrix of n directions in the positive orthant of another Euclidean space of possibly different dimension. Finding this factor therefore amounts to angle packing and finding an appropriate embedding dimension. Neither the embedding dimension nor the directions may be unique, and so many cp factorizations of the same given matrix may coexist. Using a bordering approach, and building upon an already known cp factorization of a principal block, we establish sufficient conditions under which we can extend this cp factorization to the full matrix. Simulations show that the approach is promising also in higher dimensions.

Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students’ spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains – specifically for problem types expected to show gains from spatial training – and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.

Compositional data, as they typically appear in geochemistry in terms of concentrations of chemical elements in soil samples, need to be expressed in log-ratio coordinates before applying the traditional statistical tools if the relative structure of the data is of primary interest. There are different possibilities for this purpose, like centered log-ratio coefficients, or isometric log-ratio coordinates. In both the approaches, geometric means of the compositional parts are involved, and it is unclear how measurement errors or detection limit problems affect their presentation in coordinates. This problem is investigated theoretically by making use of the theory of error propagation. Due to certain limitations of this approach, the effect of error propagation is also studied by means of simulations. This allows to provide recommendations for practitioners on the amount of error and on the expected distortion of the results, depending on the purpose of the analysis.

Myocardial stiffness is a valuable clinical biomarker for the monitoring and stratification of heart failure (HF). Cardiac finite element models provide a biomechanical framework for the assessment of stiffness through the determination of the myocardial constitutive model parameters. The reported parameter intercorrelations in popular constitutive relations, however, obstruct the unique estimation of material parameters and limit the reliable translation of this stiffness metric to clinical practice. Focusing on the role of the cost function (CF) in parameter identifiability, we investigate the performance of a set of geometric indices (based on displacements, strains, cavity volume, wall thickness and apicobasal dimension of the ventricle) and a novel CF derived from energy conservation. Our results, with a commonly used transversely isotropic material model (proposed by Guccione et al.), demonstrate that a single geometry-based CF is unable to uniquely constrain the parameter space. The energy-based CF, conversely, isolates one of the parameters and in conjunction with one of the geometric metrics provides a unique estimation of the parameter set. This gives rise to a new methodology for estimating myocardial material parameters based on the combination of deformation and energetics analysis. The accuracy of the pipeline is demonstrated in silico, and its robustness in vivo, in a total of 8 clinical data sets (7 HF and one control). The mean identified parameters of the Guccione material law were \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=3000\pm 1700\,\hbox {Pa}$$\end{document}C1=3000±1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =45\pm 25$$\end{document}α=45±25 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=25\pm 14$$\end{document}bf=25±14, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=11\pm 6$$\end{document}bft=11±6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=9\pm 5$$\end{document}bt=9±5) for the HF cases and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_1=1700\,\hbox {Pa}$$\end{document}C1=1700Pa and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =15$$\end{document}α=15 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_f=8$$\end{document}bf=8, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{ft}=4$$\end{document}bft=4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_{t}=3$$\end{document}bt=3) for the healthy case.

Cost and effect data often have missing data because economic evaluations are frequently added onto clinical studies where cost data are rarely the primary outcome. The objective of this article was to investigate which multiple imputation strategy is most appropriate to use for missing cost-effectiveness data in a randomized controlled trial. Three incomplete data sets were generated from a complete reference data set with 17, 35 and 50 % missing data in effects and costs. The strategies evaluated included complete case analysis (CCA), multiple imputation with predictive mean matching (MI-PMM), MI-PMM on log-transformed costs (log MI-PMM), and a two-step MI. Mean cost and effect estimates, standard errors and incremental net benefits were compared with the results of the analyses on the complete reference data set. The CCA, MI-PMM, and the two-step MI strategy diverged from the results for the reference data set when the amount of missing data increased. In contrast, the estimates of the Log MI-PMM strategy remained stable irrespective of the amount of missing data. MI provided better estimates than CCA in all scenarios. With low amounts of missing data the MI strategies appeared equivalent but we recommend using the log MI-PMM with missing data greater than 35 %.

The aim of the study was to construct the model forecasting the birch pollen season characteristics in Cracow on the basis of an 18-year data series. The study was performed using the volumetric method (Lanzoni/Burkard trap). The 98/95 % method was used to calculate the pollen season. The Spearman's correlation test was applied to find the relationship between the meteorological parameters and pollen season characteristics. To construct the predictive model, the backward stepwise multiple regression analysis was used including the multi-collinearity of variables. The predictive models best fitted the pollen season start and end, especially models containing two independent variables. The peak concentration value was predicted with the higher prediction error. Also the accuracy of the models predicting the pollen season characteristics in 2009 was higher in comparison with 2010. Both, the multi-variable model and one-variable model for the beginning of the pollen season included air temperature during the last 10 days of February, while the multi-variable model also included humidity at the beginning of April. The models forecasting the end of the pollen season were based on temperature in March-April, while the peak day was predicted using the temperature during the last 10 days of March.

Global field power is a valuable summary of multi-channel electroencephalography data. However, global field power is biased by the noise typical of electroencephalography experiments, so comparisons of global field power on data with unequal noise are invalid. Here, we demonstrate the relationship between the number of trials that contribute to a global field power measure and the expected value of that global field power measure. We also introduce a statistical testing procedure that can be used for multi-subject, repeated-measures (also called within-subjects) comparisons of global field power when the number of trials per condition is unequal across conditions. Simulations demonstrate the effect of unequal trial numbers on global field power comparisons and show the validity of the proposed test in contrast to conventional approaches. Finally, the proposed test and two alternative tests are applied to data collected in a rapid serial visual presentation target detection experiment. The results show that the proposed test finds global field power differences in the classical P3 range; the other tests find differences in that range but also at other times including at times before stimulus onset. These results are interpreted as showing that the proposed test is valid and sensitive to real within-subject differences in global field power in multi-subject unbalanced data.

Real-time PCR (qPCR) is the principal technique for the quantification of pathogen biomass in host tissue, yet no generic methods exist for the determination of the limit of quantification (LOQ) and the limit of detection (LOD) in qPCR. We suggest using the Youden index in the context of the receiver operating characteristic (ROC) curve analysis for this purpose. The LOQ was defined as the amount of target DNA that maximizes the sum of sensitivity and specificity. The LOD was defined as the lowest amount of target DNA that was amplified with a false-negative rate below a given threshold. We applied this concept to qPCR assays for Fusarium verticillioides and Fusarium proliferatum DNA in maize kernels. Spiked matrix and field samples characterized by melting curve analysis of PCR products were used as the source of true positives and true negatives. On the basis of the analysis of sensitivity and specificity of the assays, we estimated the LOQ values as 0.11 pg of DNA for spiked matrix and 0.62 pg of DNA for field samples for F. verticillioides. The LOQ values for F. proliferatum were 0.03 pg for spiked matrix and 0.24 pg for field samples. The mean LOQ values correspond to approximately eight genomes for F. verticillioides and three genomes for F. proliferatum. We demonstrated that the ROC analysis concept, developed for qualitative diagnostics, can be used for the determination of performance parameters of quantitative PCR. peerReviewed

Correlation is ubiquitously used in gene expression analysis although its validity as an objective criterion is often questionable. If no normalization reflecting the original mRNA counts in the cells is available, correlation between genes becomes spurious. Yet the need for normalization can be bypassed using a relative analysis approach called log-ratio analysis. This approach can be used to identify proportional gene pairs, i.e. a subset of pairs whose correlation can be inferred correctly from unnormalized data due to their vanishing log-ratio variance. To interpret the size of non-zero log-ratio variances, a proposal for a scaling with respect to the variance of one member of the gene pair was recently made by Lovell et al. Here we derive analytically how spurious proportionality is introduced when using a scaling. We base our analysis on a symmetric proportionality coefficient (briefly mentioned in Lovell et al.) that has a number of advantages over their statistic. We show in detail how the choice of reference needed for the scaling determines which gene pairs are identified as proportional. We demonstrate that using an unchanged gene as a reference has huge advantages in terms of sensitivity. We also explore the link between proportionality and partial correlation and derive expressions for a partial proportionality coefficient. A brief data-analysis part puts the discussed concepts into practice. The authors were supported by CRG internal funds provided by the Catalan Government. I. E. was also paid by the Spanish Ministerio de Economía y Competitividad under Grant BFU2011-28575.

To improve the efficacy of the in-house validation of GMO detection methods (DNA isolation and real-time PCR, polymerase chain reaction), a study was performed to gain insight in the contribution of the different steps of the GMO detection method to the repeatability and in-house reproducibility. In the present study, 19 methods for (GM) soy, maize canola and potato were validated in-house of which 14 on the basis of an 8-day validation scheme using eight different samples and five on the basis of a more concise validation protocol. In this way, data was obtained with respect to the detection limit, accuracy and precision. Also, decision limits were calculated for declaring non-conformance (>0.9%) with 95% reliability. In order to estimate the contribution of the different steps in the GMO analysis to the total variation variance components were estimated using REML (residual maximum likelihood method). From these components, relative standard deviations for repeatability and reproducibility (RSDr and RSDR) were calculated. The results showed that not only the PCR reaction but also the factors ‘DNA isolation’ and ‘PCR day’ are important factors for the total variance and should therefore be included in the in-house validation. It is proposed to use a statistical model to estimate these factors from a large dataset of initial validations so that for similar GMO methods in the future, only the PCR step needs to be validated. The resulting data are discussed in the light of agreed European criteria for qualified GMO detection methods. Electronic supplementary material The online version of this article (doi:10.1007/s00216-009-3315-6) contains supplementary material, which is available to authorized users.

The paper presents a new scenario-based decision rule for the classical version of the newsvendor problem (NP) under complete uncertainty (i.e. uncertainty with unknown probabilities). So far, NP has been analyzed under uncertainty with known probabilities or under uncertainty with partial information (probabilities known incompletely). The novel approach is designed for the sale of new, innovative products, where it is quite complicated to define probabilities or even probability-like quantities, because there are no data available for forecasting the upcoming demand via statistical analysis. The new procedure described in the contribution is based on a hybrid of Hurwicz and Bayes decision rules. It takes into account the decision maker’s attitude towards risk (measured by coefficients of optimism and pessimism) and the dispersion (asymmetry, range, frequency of extremes values) of payoffs connected with particular order quantities. It does not require any information about the probability distribution.

We propose the use of parametric bootstrap methods to investigate the finite sample distribution of the maximum likelihood estimator for the parameter vector of a stochastic mortality model. Particular emphasis is placed on the effect that the size of the underlying population has on the distribution of the MLE in finite samples, and on the dependency structure of the resulting estimator: that is, the dependencies between estimators for the age, period and cohort effects in our model. In addition, we study the distribution of a likelihood ratio test statistic where we test a null hypothesis about the true parameters in our model. Finally, we apply the LRT to the cohort effects estimated from observed mortality rates for females in England and Wales and males in Scotland.

Composting is one of the integrated waste management strategies used for the recycling of organic wastes into a useful product. Composting methods vary in duration of decomposition and potency of stability, maturity and sanitation. This study was aimed to investigate the comparative effectiveness of four different methods of composting viz. windrow composting (WC), Vermicomposting (VC), pit composting (PC) and combined windrow and vermicomposting (WVC) on the stabilization, maturation and sanitization of mixtures of municipal solid organic waste and dried faecal sludge. The composting treatments were arranged in a completely randomized block design with three replications. The changes in physico-chemical and biological characteristics of the compost were examined at 20 days interval for 100 days using standard laboratory procedures. The analysis of variance was performed using SAS software and the significant differences were determined using Fisher’s LSD test at P ≤ 0.05 level. The evolution of composting temperature, pH, EC, $${\text{NH}}_{ 4}^{ + }$$ , $${\text{NO}}_{ 3}^{ - }$$ , $${\text{NH}}_{ 4}^{ + }$$ : $${\text{NO}}_{ 3}^{ - }$$ ratio, OC, C:N ratio and total volatile solids varied significantly among the composting methods and with composting time. The evolution of total nitrogen and germination index also varied significantly (P ≤ 0.001) with time, but their variation among the composting methods was not significant (P > 0.05). Except for PC, all other methods of composting satisfied all the indices for stability/maturity of compost at the 60th day of sampling; whereas PC achieved the critical limit values for most of the indices at the 80th day. A highly significant differences (P ≤ 0.001) were noted among the composting methods with regard to their effectiveness in eliminating pathogens (faecal coliforms and helminth eggs). The WVC method was most efficient in eliminating the pathogens complying with WHO’s standard. Turned windrow composting and composting involving earthworms hastened the biodegradation process of organic wastes and result in the production of stable compost earlier than the traditional pit method of composting. The WVC method is most efficient in keeping the pathogens below the threshold level. Thus, elimination of pathogens from composts being a critical consideration, this study would recommend this method for composting organic wastes involving human excreta.

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

The purpose of a seed train is the generation of an adequate number of cells for the inoculation of a production bioreactor. This is time- and cost-intensive: From volumes used for cell thawing or cell line maintenance the cell number has to be increased. The cells are usually run through many cultivation systems which become larger with each passage (e.g. T-flasks, roller bottles or shake flasks, small scale bioreactor systems and subsequently larger bioreactors. Single-use systems may be applied and systems which are inoculated at a partly filled state and culture volume is increased afterwards by medium addition). The production bioreactor is inoculated out of the largest seed train scale.

The mathematical analysis of the shape of chemical reactors is studied in this paper through the research of the optimization of its effectiveness η such as introduced by R. Aris around 1960. Although our main motivation is the consideration of reactors specially designed for the treatment of wastewaters our results are relevant also in more general frameworks. We simplify the modeling by assuming a single chemical reaction with a monotone kinetics leading to a parabolic equation with a non-necessarily differentiable function. In fact we consider here the case of a single, non-reversible catalysis reaction of chemical order q,00). We assume the chemical reactor of cylindrical shape Ω=G×(0,H) with G and open regular set of R2 not necessarily symmetric. We show that among all the sections G with prescribed area the ball is the set of lowest effectiveness η(t,G). The proof uses the notions of Steiner rearrangement. Finally, we show that if the height H is small enough then the effectiveness can be made as close to 1 as desired. 888 The mathematical analysis of the shape of chemical reactors is studied in this paper through the research of the optimization of its effectiveness (Formula presented.) such as introduced by R. Aris around 1960. Although our main motivation is the consideration of reactors specially designed for the treatment of wastewaters our results are relevant also in more general frameworks. We simplify the modeling by assuming a single chemical reaction with a monotone kinetics leading to a parabolic equation with a non-necessarily differentiable function. In fact we consider here the case of a single, non-reversible catalysis reaction of chemical order (Formula presented.) (i.e., the kinetics is given by (Formula presented.) for some (Formula presented.)). We assume the chemical reactor of cylindrical shape (Formula presented.) with G and open regular set of (Formula presented.) not necessarily symmetric. We show that among all the sections G with prescribed area the ball is the set of lowest effectiveness (Formula presented.). The proof uses the notions of Steiner rearrangement. Finally, we show that if the height H is small enough then the effectiveness can be made as close to 1 as desired.

This paper studies the one-to-one two-sided marriage model (Gale and Shapley 1962). If agents’ preferences exhibit mutually best (i.e., each agent is most preferred by her/his most preferred matching partner), there is a unique stable matching without rank gaps (i.e., in each matched pair the agents assign one another the same rank). We study in how far this result is robust for matching markets that are “close” to mutually best. Without a restriction on preference profiles, we find that natural “distances” to mutually best neither bound the size of the core nor the rank gaps at stable matchings. However, for matching markets that satisfy horizontal heterogeneity, “local” distances to mutually best provide bounds for the size of the core and the rank gaps at stable matchings., The first draft of this paper was written while F. Klijn was LFUI guest professor at Innsbruck University. He gratefully acknowledges the hospitality of Innsbruck University and support from AGAUR-Generalitat de Catalunya (2017-SGR-1359), Ministerio de Ciencia, Innovación y Universidades (ECO2017-88130-P), and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563 and CEX2019-000915-S). C. Kah and M. Walzl thank the Austrian Science Foundation (FWF) for support through project P-28632-G27 and SFB63.

Given an infinite family of extended real-valued functions fi, i∈I, and a family H of nonempty finite subsets of I, the H-partial robust sum of fi, i∈I, is the supremum, for J∈H, of the finite sums ∑j∈Jfj. These infinite sums arise in a natural way in location problems as well as in functional approximation problems, and include as particular cases the well-known sup function and the so-called robust sum function, corresponding to the set H of all nonempty finite subsets of I, whose unconstrained minimization was analyzed in previous papers of three of the authors (https://doi.org/10.1007/s11228-019-00515-2 and https://doi.org/10.1007/s00245-019-09596-9). In this paper, we provide ordinary and stable zero duality gap and strong duality theorems for the minimization of a given H-partial robust sum under constraints, as well as closedness and convex criteria for the formulas on the subdifferential of the sup-function. This research was supported by the National Foundation for Science & Technology Development (NAFOSTED), Vietnam, Project 101.01-2018.310, and by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI), and European Regional Development Fund (ERDF), Project PGC2018-097960-B-C22.

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space Rn (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two significant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdifferentials, recovering known results in both fields and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of infinite sets of sites by appealing to well-known results on linear semi-infinite systems. This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); by CONICET, Argentina, Res D No 4198/17; and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3922/19-R, Cod.06/D227, Argentina.

The final version is published in Complex Analysis and Operator Theory, 13-No.6, (2019). Received: 8 May 2018 / Accepted: 24 December 2018 / Published online: 11 January 2019. Acknowledgment: The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Funda¸c˜ao para a Ciˆencia e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden f¨ur instation¨are PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de A¸c˜oes Integradas Luso-Alem˜as 2017” - DAAD-CRUP - Ação No. A-15/17 / DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014). In this paper, we develop a time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems. UID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014 info:eu-repo/semantics/publishedVersion

This paper introduces a new temperature index, which can suitably represent the underlying of a weather derivative. Such an index is defined as the weighted mean of daily average temperatures measured in different locations. It may be used to hedge volumetric risk, that is the effect of unexpected fluctuations in the demand/supply for some specific commodities—of agricultural or energy type, for example—due to unfavorable temperature conditions. We aim at exploring the long term memory property of the volatility of such an index, in order to assess whether there exist some long-run paths and regularities in its riskiness. The theoretical part of the paper proceeds in a stepwise form: first, the daily average temperatures are modeled through autoregressive dynamics with seasonality in mean and volatility; second, the assessment of the distributional hypotheses on the parameters of the model is carried out for analyzing the long term memory property of the volatility of the index. The theoretical results suggest that the single terms of the index drive the long memory of the overall aggregation; moreover, interestingly, the proper selection of the parameters of the model might lead both to cases of persistence and antipersistence. The applied part of the paper provides some insights on the behaviour of the volatility of the proposed index, which is built starting from single daily average temperature time series.

This paper presents a DIRECT-type method that uses a filter methodology to assure convergence to a feasible and optimal solution of nonsmooth and nonconvex constrained global optimization problems. The filter methodology aims to give priority to the selection of hyperrectangles with feasible center points, followed by those with infeasible and non-dominated center points and finally by those that have infeasible and dominated center points. The convergence properties of the algorithm are analyzed. Preliminary numerical experiments show that the proposed filter-based DIRECT algorithm gives competitive results when compared with other DIRECT-type methods., The authors would like to thank two anonymous referees and the Associate Editor for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ciência e Tecnologia within the projects UID/CEC/00319/2013 and ˆ UID/MAT/00013/2013., info:eu-repo/semantics/publishedVersion

The algebraic approach by E.W. Dijkstra and C.S. Scholten to formal logic is a proof calculus, where the notion of proof is a sequence of equivalences proved – mainly – by using substitution of ‘equals for equals’. This paper presents Set , a first-order logic axiomatization for set theory using the approach of Dijkstra and Scholten. What is novel about the approach presented in this paper is that symbolic manipulation of formulas is an effective tool for teaching an axiomatic set theory course to sophomore-year undergraduate students in mathematics. This paper contains many examples on how argumentative proofs can be easily expressed in Set and points out how the rigorous approach of Set can enrich the learning experience of students. The results presented in this paper are part of a larger effort to formally study and mechanize topics in mathematics and computer science with the algebraic approach of Dijkstra and Scholten., El enfoque algebraico de E.W. Dijkstra y C.S. Scholten a la lógica formal es un cálculo de prueba, donde la noción de prueba es una secuencia de equivalencias probadas, principalmente, mediante la sustitución de "iguales por iguales". Este artículo presenta Set, una axiomatización lógica de primer orden para la teoría de conjuntos utilizando el enfoque de Dijkstra y Scholten. Lo novedoso del enfoque presentado en este artículo es que la manipulación simbólica de fórmulas es una herramienta eficaz para enseñar un curso de teoría axiomática de conjuntos a estudiantes de segundo año de pregrado en matemáticas. Este artículo contiene muchos ejemplos sobre cómo las pruebas argumentativas se pueden expresar fácilmente en Set y señala cómo el enfoque riguroso de Set puede enriquecer la experiencia de aprendizaje de los estudiantes. Los resultados presentados en este artículo son parte de un esfuerzo mayor para estudiar y mecanizar formalmente temas en matemáticas e informática con el enfoque algebraico de Dijkstra y Scholten., Colombian Conference on Computing

In this paper we introduce a generalization of the Marshall-Olkin distribution that allows for some dependence among the shock arrival times while it preserves exponentially distributed observed lifetimes: these features make the resulting distribution well suited for credit risk applications. The main result of the paper is that the only Archimedean dependence structure consistent with these requirements is the Gumbel one.

This paper is concerned with the boundary stabilization problem of first-order hyperbolic equations with input delay. In our previous work, the same problem for parabolic equations with input delay was addressed. For the hyperbolic equation, the element of time lag is similarly replaced by a transport equation and a backstepping method is employed. However, unlike in the case of the parabolic equation, it is difficult to obtain the eigenvalues and eigenfunctions of the system operator for the hyperbolic equation. Hence, we cannot construct the target system and the controller by using the finite-dimensional control theory together. In this paper, using $$C_0$$ -semigroups for hyperbolic equations with nonlocal boundary condition, we show that the proposed controller is expressed by an abstract form in a Hilbert space so-called a predictor, and that the predictor makes sense under a condition. Further, for the inverse integral transformation, we obtain an interesting result on its continuity under the same condition. A numerical algorithm is also proposed for solving a non-standard hyperbolic equation appearing in our controller design.

The aim of this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on variable exponent Morrey spaces of an integral form. As an application of the boundedness of the maximal operator, we establish Sobolev-type inequalities for Riesz potentials $$I_{\alpha (\cdot )}f$$ of variable order $$\alpha (\cdot )$$ of functions f in variable exponent Morrey spaces of an integral form.

We investigate the total number of edge crossings (i.e., the crossing number) of the Euclidean minimum weight Laman graph \(\mathsf {MLG}(P)\) on a planar point set P. Bereg et al. (2016) showed that the upper and lower bounds for the crossing number of \(\mathsf {MLG}(P)\) are \(6|P|-9\) and \(|P|-3\), respectively. In this paper, we improve these upper and lower bounds given by Bereg et al. (2016) to \(2.5|P|-5\) and \((1.25-\varepsilon )|P|\) for any \(\varepsilon > 0\), respectively. Especially, for improving the upper bound, we introduce a novel counting scheme based on some geometric observations.

The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability. Results are illustrated by examples. The paper deals with systems of linear differential equations with coefficients depending on the Markov process. Equations for particular density and the moment equations for given systems are derived and used in the investigation of solvability of initial problems and stability. Results are illustrated by examples.

In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times. In healthcare, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. The Coxian phase-type distribution has not only been shown to provide a good representation of real survival data, but its interpretation seems reasonably initiative to the medical experts. The drawback, however, is fitting the distribution to the data. There have been many attempts at accurately estimating the Coxian phase-type parameters. This paper wishes to examine the most promising of the approaches reported in the literature to determine the most accurate. Three performance measures are introduced to assess the fitting process of the algorithms along with the likelihood values and AIC to examine the goodness of fit and complexity of the model. Previous research suggests that the fitting process is strongly influenced by the initial parameter estimates and the data itself being quite variable. To overcome this, one experiment in this research paper will use the same initial parameter values for each estimation and perform the fits on the data simulated from a Coxian phase-type distribution with known parameters.

This paper deals with functional equations in the form of $f(x) + g(y) = h(x,y)$ where $h$ is given and $f$ and $g$ are unknown. We will show that if $h$ is a Borel measurable function associated with characterizations of the uniform or Cauchy distributions, then there is no measurable solutions of the equation. Our proof uses a characterization of the Dirac measure and it is also applicable to the arctan equation., Comment: 7 pages, to appear in Aequationes mathematicae

In this paper, D-optimal chemical balance weighing designs with three objects are considered. The error terms are assumed to form a first-order autoregressive process, which implies that the covariance matrix of the vector of errors depends on the known parameter $$\rho $$ . It is shown that the designs constructed by Katulska and Smaga (Metrika 76:393–407, 2013) are still D-optimal weighing designs with three objects under a wider interval of possible values for parameter $$\rho $$ than that considered in that paper. Those designs are also proved to be highly D-efficient designs, when D-optimal design is not known.

In the research of optimization problems, optimality conditions play an important role. By using some derivatives, various types of necessary and/or sufficient optimality conditions have been introduced by many researchers. Especially, in convex programming, necessary and sufficient optimality conditions in terms of the subdifferential have been studied extensively. Recently, necessary and sufficient optimality conditions for quasiconvex programming have been investigated by the authors. However, there are not so many results concerned with Karush–Kuhn–Tucker type optimality conditions for non-differentiable quasiconvex programming. In this paper, we study a Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. We show some closedness properties for Greenberg–Pierskalla subdifferential. Under the Slater constraint qualification, we show a necessary and sufficient optimality condition for essentially quasiconvex programming in terms of Greenberg–Pierskalla subdifferential. Additionally, we introduce a necessary and sufficient constraint qualification of the optimality condition. As a corollary, we show a necessary and sufficient optimality condition for convex programming in terms of the subdifferential.

The purpose of this paper is to introduce the concept of fuzzy variational- like inequalities and to study the existence problem and the iterative approximation problem for solutions of certain kinds of fuzzy variational- like inequalities in Hilbert spaces. By using the general auxiliary principle technique, Ky Fan's KKM theorem, Nadler's fixed point theorem, and some new analytic techniques, some existence theorems and some iterative approximation schemes for solving this kind of fuzzy variational- like inequalities are established. The results presented in this paper are new and they generalize, improve, and unify a number of recent results.

This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family. The research of the first author is supported by ANID-Fondecyt 1190012, Proyecto/Grant PIA AFB-170001, MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA- GAL 18/00205). The second author is supported by the Research Project PGC2018-097960-B-C21 from MICINN, Spain, and by the Australian ARC—Discovery Projects DP 180100602.

Let $${\mathcal {M}}$$ M denote the maximal ideal of the ring of integers of a non-Archimedean field K with residue class field k whose invertible elements, we denote $$k^{\times }$$ k × , and a uniformizer we denote $$\pi $$ π . In this paper, we consider the map $$T_{v}: {\mathcal {M}} \rightarrow {\mathcal {M}}$$ T v : M → M defined by $$\begin{aligned} T_v(x) = \frac{\pi ^{v(x)}}{x} - b(x), \end{aligned}$$ T v ( x ) = π v ( x ) x - b ( x ) , where b(x) denotes the equivalence class to which $$\frac{\pi ^{v(x)}}{x}$$ π v ( x ) x belongs in $$k^{\times }$$ k × . We show that $$T_v$$ T v preserves Haar measure $$\mu $$ μ on the compact abelian topological group $${\mathcal {M}}$$ M . Let $${\mathcal {B}}$$ B denote the Haar $$\sigma $$ σ -algebra on $${\mathcal {M}}$$ M . We show the natural extension of the dynamical system $$({\mathcal {M}}, {\mathcal {B}}, \mu , T_v)$$ ( M , B , μ , T v ) is Bernoulli and has entropy $$\frac{\#( k)}{\#( k^{\times })}\log (\#( k))$$ # ( k ) # ( k × ) log ( # ( k ) ) . The first of these two properties is used to study the average behaviour of the convergents arising from $$T_v$$ T v . Here for a finite set A its cardinality has been denoted by $$\# (A)$$ # ( A ) . In the case $$K = {\mathbb {Q}}_p$$ K = Q p , i.e. the field of p-adic numbers, the map $$T_v$$ T v reduces to the well-studied continued fraction map due to Schneider.

We consider the preferential attachment model with location-based choice introduced by Haslegrave et al. (Random Struct Algorithms 56(3):775–795, 2020) as a model in which condensation phenomena can occur. In this model, each vertex carries an independent and uniformly distributed location. Starting from an initial tree, the model evolves in discrete time. At every time step, a new vertex is added to the tree by selectingrcandidate vertices from the graph with replacement according to a sampling probability proportional to these vertices’ degrees. The new vertex then connects to one of the candidates according to a given probability associated to the ranking of their locations. In this paper, we introduce a function that describes the phase transition when condensation can occur. Considering the noncondensation phase, we use stochastic approximation methods to investigate bounds for the (asymptotic) proportion of vertices inside a given interval of a given maximum degree. We use these bounds to observe a power law for the asymptotic degree distribution described by the aforementioned function. Hence, this function fully characterises the properties we are interested in. The power law exponent takes the critical value one at the phase transition between the condensation–noncondensation phase.

Using the variational method, Chenciner and Montgomery (2000 Ann. Math. 152 881–901) proved the existence of an eight-shaped orbit of the planar three-body problem with equal masses. Since then a number of solutions to the N-body problem have been discovered. On the other hand, symbolic dynamics is one of the most useful methods for understanding chaotic dynamics. The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and was studied by using symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). In this paper, we study the limiting case of the Sitnikov problem. By using the variational method, we show the existence of various kinds of solutions in the planar Sitnikov problem. For a given symbolic sequence, we show the existence of orbits realizing it. We also prove the existence of periodic orbits.

The aim of this paper is to investigate a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3-space is a Willmore surface, its conformal Gauss map is harmonic and a dressing on the conformal Gauss map can be defined. We study the induced transformation on minimal surfaces in the simplest case, the simple factor dressing, and show that the well-known Lopez–Ros deformation of minimal surfaces is a special case of this transformation. We express the simple factor dressing and the Lopez–Ros deformation explicitly in terms of the minimal surface and its conjugate surface. In particular, we can control periods and end behaviour of the simple factor dressing. This allows to construct new examples of doubly-periodic minimal surfaces arising as simple factor dressings of Scherk’s first surface.

In this paper we first extend from normed spaces to locally convex spaces some characterizations of denting points in convex sets. On the other hand, we also prove that in an infrabarreled locally convex space a point in a convex set is denting if and only if it is a point of continuity and an extreme point of the closure of such a convex set under the strong topology in the second dual. The version for normed spaces of the former equivalence is new and contains, as particular cases, some known and remarkable results. We also extend from normed spaces to locally convex spaces some known characterizations of the weak property (π) of cones. Besides, we provide some new results regarding the angle property of cones and related. We also state that the class of cones in normed spaces having a pointed completion is the largest one for which the vertex is a denting point if and only if it is a point of continuity. Finally we analyse and answer several problems in the literature concerning geometric properties of cones which are related with density problems into vector optimization. The authors Fernando García-Castaño and M. A. Melguizo Padial have been supported by MINECO and FEDER (MTM2017-86182-P).

We consider a fractional order viscoelasticity problem modelled by a power-law type stress relaxation function. This viscoelastic problem is a Volterra integral equation of the second kind with a weakly singular kernel where the convolution integral corresponds to fractional order differentiation/integration. We use a spatial finite element method and a finite difference scheme in time. Due to the weak singularity, fractional order integration in time is managed approximately by linear interpolation so that we can formulate a fully discrete problem. In this paper, we present a stability bound as well as a priori error estimates. Furthermore, we carry out numerical experiments with varying regularity of exact solutions at the end., Accepted by Advances in Computational Mathematics

In this paper we have given conditions on exponential polynomials $$P_{n}(s)$$ of Dirichlet type to be attained the equality between each of two pairs of bounds, called essential bounds, $$a_{P_{n}(s)}$$ , $$\rho _{N}$$ and $$b_{P_{n}(s)}$$ , $$\rho _{0}$$ associated with $$P_{n}(s)$$ . The reciprocal question has been also treated. The bounds $$a_{P_{n}(s)}$$ , $$b_{P_{n}(s)}$$ are defined as the end-points of the minimal closed and bounded real interval $$I= [ a_{P_{n}(s)},b_{P_{n}(s)} ] $$ such that all the zeros of $$P_{n}(s)$$ are contained in the strip $$I\times {\mathbb {R}}$$ of the complex plane $${\mathbb {C}}$$ . The bounds $$\rho _{N}$$ , $$\rho _{0}$$ are defined as the unique real solutions of Henry equations of $$P_{n}(s)$$ . Some applications to the partial sums of the Riemann zeta function have been also showed.

We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\lambda$)EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability $p$. We present refined results for the expected optimisation time of the (1+1)EA and the (1+$\lambda$)EA on the function LeadingOnes, where bits have to be optimised in sequence. Previous work showed that the (1+1)EA on LeadingOnes runs in polynomial expected time if $p = O((\log n)/n^2)$ and needs superpolynomial expected time if $p = \omega((\log n)/n)$, leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is $\Theta(n^2) \cdot \exp(\Theta(\min\{pn^2, n\}))$ for all $p \le 1/2$, allowing for the first time to locate the threshold between polynomial and superpolynomial expected times at $p = \Theta((\log n)/n^2)$. Hence the (1+1)EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that offspring populations of size $\lambda \ge 3.42\log n$ can effectively deal with much higher noise than known before. Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient. We prove that in this particular setting noise can have a highly beneficial effect on performance., Comment: This is an extended version of a paper that appeared in the Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2018), https://doi.org/10.1145/3205455.3205595

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92–106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

Based on Bohr’s equivalence relation for general Dirichlet series, in this paper we connect the families of equivalent exponential polynomials with a geometrical point of view related to lines in crystal-like structures. In particular we characterize this equivalence relation, and give an alternative proof of Bochner’s property referring to these functions, through this new geometrical perspective. The first author’s research was partially supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms. This theory has important applications in optimal control theory for Herglotz control problems, in which the cost function is given implicitly, through an ODE, instead of by a definite integral. Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics., M. de León and M. Lainz acknowledge the partial finantial support from MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa project SEV-2015-0554. M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. M.C. Muñoz-Lecanda acknowledges the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades project PGC2018-098265-B-C33 and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932.

This paper presents a full generalization of Bohr’s equivalence theorem for the case of almost periodic functions, which improves a recent result that was uniquely formulated in the case of existence of an integral basis for the set of exponents of the associated Dirichlet series. J.M. Sepulcre research was partially supported by MICIU of Spain under Project Number PGC2018-097960-B-C22.

First-exit problems for the Brownian motion (W(t)) or general diffusion processes, have important applications. Given a boundary b(t), the distribution of the first-exit time $$\tau $$ τ has to be computed, in most cases numerically. In the inverse first-passage-time problems, the distribution of $$\tau $$ τ is given and the boundary b has to be found. The boundary and the density of $$\tau $$ τ satisfy a Volterra integral equation. Again numerical methods approximate the solution b for given distribution of $$\tau $$ τ . We propose and analyze estimators of b for a given sample $$\tau _1,\ldots ,\tau _n$$ τ 1 , … , τ n of first-exit times. The first estimator, the empirical estimator, is the solution of a stochastic version of the Volterra equation. We prove that it is strongly consistent and we derive an upper bound for its asymptotics convergence rate. Finally, this estimator is compared to a Bayesian estimator, which is based on an approximate likelihood function. Monte Carlo experiments suggests that the empirical estimator is simple, computationally manageable and outperforms the alternative procedure considered in this paper.

In this paper we will get a class of functional equations involving a countable set of terms, summed by the well known Bochner–Fejér summation procedure, which are closely associated with the set of almost periodic functions. We will show that the zeros of a prefixed almost periodic function determine analytic solutions of such a functional equation associated with it, and we will obtain other solutions which are analytic or meromorphic on a certain domain. J. M. Sepulcre was supported by PGC2018-097960-B-C22 (MCIU/AEI/ERDF, UE).