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We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously decides (without knowing Proposer's choice) whether to add it to the graph. Proposer cannot propose an edge which would create a triangle in the graph. The game ends when Proposer has no legal moves remaining, and Proposer wins if the final graph has independence number at least $s$. We prove a threshold phenomenon exists for this game by exhibiting randomized strategies for both players that are optimal up to constants. Namely, there exist constants $0B\sqrt{n}\log{n}$. This is a factor of $\Theta(\sqrt{\log{n}})$ larger than the lower bound coming from the off-diagonal Ramsey number $r(3,s)$.

Many commercial materials (papers and boards) contain optical brightening agents also known as fluorescent whitening agents. Adequate adjustment of the UV content of a measurement device (e.g., spectrophotometers) is essential for accurate color measurement. As specified in the ISO standards, the UV content is adjusted against an assigned value of an international reference transfer standard, for example, CIE whiteness (D65/10°) for the CIE illuminant D65 or ISO brightness for the C illuminant. Because of the simplicity, these approaches have gained great popularity in papermaking industry. Yet, there has been little evidence indicating how accurate the total spectral radiance factor corresponding to the single assigned value is reproduced. Hence, we present a method that quantitatively evaluates the accuracy of the UV-adjustment technique, through comparing the total spectral radiance factors obtained from UV adjustment with the assigned ones. This method has been applied to three second-level international reference transfer standard illuminated by three standard illuminants, D65, C, and D50. We found that the major differences between the assigned spectra and those obtained from the UV adjustments occur in the blue band where fluorescence is strong. At a few wavelengths, the differences may be up to 4–5%. Nevertheless, their color differences corresponding to the assigned spectra and those obtained from the UV adjustments are still smaller than unity (1 ΔE*) for all of the illumination conditions. Two instruments using the representative UV adjusting techniques, for example, the conventional UV-adjusting with an adjustable (GG395) UV filter and the numerical UV-filtering, have been studied. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 19–26, 2017

Discussion of the Paper "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models" by Soren Johansen and Bent Nielsen

OBJECTIVES Current human infant urine collection methods for the field are problematic for the researcher and potentially uncomfortable for the infant. In this study, we compared two minimally invasive methods for collecting infant urine: organic cotton balls and filter paper. MATERIALS AND METHODS We first collected urine from infants using the clean catch method. We then used those samples to compare the performance of filter paper and cotton ball collection protocols. We analyzed the clean catch and cotton samples using commercial estrone-3-glucuronide (E1G) kits and tried two different extraction methods for the filter paper. Using a paired t-test (n = 10), we compared clean catch and cotton samples. We also compared effect sizes within and between methods. RESULTS We were unable to extract enough urine from the filter paper to successfully assay the samples for E1G. The paired t-test revealed a statistically significant difference between the clean catch and cotton methods (t = 2.63, p-value = 0.03). However, the effect size was small (5.91 μg/ml, n = 10, 95% CI = 3.80, 8.02) and similar to or larger than the difference seen between duplicate wells for clean catch and cotton values. DISCUSSION While this study is limited by sample size, our results indicate that filter paper is not a field-friendly method for collecting infant urine. However, we found that organic cotton balls showed similar values to the clean catch method, and we propose this method as an alternative, minimally invasive method for study of E1G in human infant urine.

In this work, we developed a robust permutation test for the concordance correlation coefficient (ρ c) for testing the general hypothesis H 0 : ρ c = ρ c(0). The proposed test is based on an appropriately studentized statistic. Theoretically, the test is proven to be asymptotically valid in the general setting when two paired variables are uncorrelated but dependent. This desired property was demonstrated across a range of distributional assumptions and sample sizes in simulation studies, where the test exhibits robust type I error control in all settings tested, even when the sample size is small. We demonstrated the application of this test in two real world examples across cardiac output measurements and endocardiographic imaging.

The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.

Estimating the effectiveness of protected areas (PAs) in reducing deforestation is useful to support decisions on whether to invest in better management of areas already protected or to create new ones. Statistical matching is commonly used to assess this effectiveness, but spatial autocorrelation and regional differences in protection effectiveness are frequently overlooked. Using Colombia as a case study, we employed statistical matching to account for confounding factors in park location and accounted for for spatial autocorrelation to determine statistical significance. We compared the performance of different matching procedures—ways of generating matching pairs at different scales—in estimating PA effectiveness. Differences in matching procedures affected covariate similarity between matched pairs (balance) and estimates of PA effectiveness in reducing deforestation. Independent matching yielded the greatest balance. On average 95% of variables in each region were balanced with independent matching, whereas 33% of variables were balanced when using the method that performed worst. The best estimates suggested that average deforestation inside protected areas in Colombia was 40% lower than in matched sites. Protection significantly reduced deforestation, but PA effectiveness differed among regions. Protected areas in Caribe were the most effective, whereas those in Orinoco and Pacific were least effective. Our results demonstrate that accounting for spatial autocorrelation and using independent matching for each subset of data is needed to infer the effectiveness of protection in reducing deforestation. Not accounting for spatial autocorrelation can distort the assessment of protection effectiveness, increasing type I and II errors and inflating effect size. Our method allowed improved estimates of protection effectiveness across scales and under different conditions and can be applied to other regions to effectively assess PA performance., Article impact statement: Spatial autocorrelation and sampling design can distort estimations of protected area effectiveness at reducing forest loss.

The spread of novel virus SARS‐CoV‐2, well known as COVID‐19 has become a major health issue currently which has turned up to a pandemic worldwide. The treatment recommendations are variable. Lack of appropriate medication has worsened the disease. On the basis of prior research, scientists are testing drugs based on medical therapies for SARS and MERS. Many drugs which include lopinavir, ritonavir and thalidomide are listed in the new recommendations. A topological index is a type of molecular descriptor that simply defines numerical values associated with the molecular structure of a compound that is effectively used in modeling many physicochemical properties in numerous quantitative structure–property/activity relationship (QSPR/QSAR) studies. In this study, several degree‐based and neighborhood degree sum‐based topological indices for several antiviral drugs were investigated by using a M‐polynomial and neighborhood M‐polynomial methods. In addition, a QSPR was established between the various topological indices and various physicochemical properties of these antiviral drugs along with remdesivir, chloroquine, hydroxychloroquine and theaflavin was performed in order to assess the efficacy of the calculated topological indices. The obtained results reveal that topological indices under study have strong correlation with the physicochemical characteristics of the potential antiviral drugs. A biological activity (pIC50) of these compounds were also investigated by using multiple linear regressions (MLR) analysis., The main results of this paper are several degree based and neighborhood degree based topological indices of antiviral drugs for the treatment of COVID‐19 like Lopinavir, Ritonavir, Arbidol and Thalidomide through M‐polynomial and NM‐polynomial by analyzing their molecular structures. Moreover it establishes a strong correlation between physicochemical properties of antiviral drugs and the topological indices tested.

The standardized mean difference is a well‐known effect size measure for continuous, normally distributed data. In this paper we present a general basis for important other distribution families. As a general concept, usable for every distribution family, we introduce the relative effect, also called Mann–Whitney effect size measure of stochastic superiority. This measure is a truly robust measure, needing no assumptions about a distribution family. It is thus the preferred tool for assumption‐free, confirmatory studies. For normal distribution shift, proportional odds, and proportional hazards, we show how to derive many global values such as risk difference average, risk difference extremum, and odds ratio extremum. We demonstrate that the well‐known benchmark values of Cohen with respect to group differences—small, medium, large—can be translated easily into corresponding Mann–Whitney values. From these, we get benchmarks for parameters of other distribution families. Furthermore, it is shown that local measures based on binary data (2 × 2 tables) can be associated with the Mann–Whitney measure: The concept of stochastic superiority can always be used. It is a general statistical value in every distribution family. It therefore yields a procedure for standardizing the assessment of effect size measures. We look at the aspect of relevance of an effect size and—introducing confidence intervals—present some examples for use in statistical practice.

Multiplicity is common in clinical studies and the current standard is to use the familywise error rate to ensure that the errors are kept at a prespecified level. In this paper, we will show that, in certain situations, familywise error rate control does not account for all errors made. To counteract this problem, we propose the use of the expected number of false claims (EFC). We will show that a (weighted) Bonferroni approach can be used to control the EFC, discuss how a study that uses the EFC can be powered for co‐primary, exchangeable, and hierarchical endpoints, and show how the weight for the weighted Bonferroni test can be determined in this manner. ©2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.

We explore the problem of variable selection in a case‐control setting with mass spectrometry proteomic data consisting of paired measurements. Each pair corresponds to a distinct isotope cluster and each component within pair represents a summary of isotopic expression based on either the intensity or the shape of the cluster. Our objective is to identify a collection of isotope clusters associated with the disease outcome and at the same time assess the predictive added‐value of shape beyond intensity while maintaining predictive performance. We propose a Bayesian model that exploits the paired structure of our data and utilizes prior information on the relative predictive power of each source by introducing multiple layers of selection. This allows us to make simultaneous inference on which are the most informative pairs and for which—and to what extent—shape has a complementary value in separating the two groups. We evaluate the Bayesian model on pancreatic cancer data. Results from the fitted model show that most predictive potential is achieved with a subset of just six (out of 1289) pairs while the contribution of the intensity components is much higher than the shape components. To demonstrate how the method behaves under a controlled setting we consider a simulation study. Results from this study indicate that the proposed approach can successfully select the truly predictive pairs and accurately estimate the effects of both components although, in some cases, the model tends to overestimate the inclusion probability of the second component.

This study assesses the techno-economic performance of production lines for obtaining 1,3-butadiene and e-caprolactam from C6 sugars. Process models were developed to assess their technical performance and to derive inputs for economic analysis. The economic assessment was carried out using net present value (NPV) and production costs as indicators. Sensitivity analyses were carried out to account for the effects of variations in inputs, such as processing capacity, valorization of humins, and prices, on the economic outputs. Results indicate that both production lines perform similarly from an energy intensity point of view (34-50 MJ/kg of main product). However, in terms of yield (kg of product per kg C6 sugar), caprolactam shows higher values by a factor of 1.6-3.6 in comparison to that of butadiene. The butadiene production line is not economically attractive, showing a negative NPV (-647 to -642 M€) and production costs 3-5 times higher than the reference market price (Case I 4369 €/tonne, Case II 3406 €/tonne). The caprolactam production line seems to be unfeasible with negative NPV (-229 M€) and production costs 30% higher than the reference price (Case III 2595 €/tonne, Case IV 1875 €/tonne). However, if the production yield is increased, the caprolactam production line becomes economically attractive with production costs 6% lower than its reference market price. The production costs of caprolactam can be further decreased if the process capacity is increased, reflecting the benefits of the economies of scale, as well as including heat and power produced from humins. Overall, the caprolactam production line shows higher economic potential.

High levels of aspalathin, an antidiabetic dihydrochalcone, in green rooibos underpins interest in the production of a standardised extract. Elements of a quality-by-design approach were applied to optimise extraction conditions, aiming at the delivery of a dry matter yield (DMY) ≥ 160 g kg-1 and an extract with an aspalathin content (AC) ≥ 80 g kg-1 .; Results: Hot water extraction parameters, namely extraction time, extraction temperature and water-to-plant material ratio, were optimised for DMY and aspalathin extraction efficiency (AEE) using Design of Experiments. Good polynomial prediction models were obtained and multiresponse desirability plots indicated 37 min, 93 °C and 23:1 as optimal conditions. Even when using 30 min and 10:1 instead for practical reasons, the target DMY and AC values could be achieved with the caveat that plant material with an AC ≥ 30 g kg-1 is used. Particle size distribution and stem content were identified as contributing to variation in the AC of raw material.; Conclusion: By setting raw material specifications in terms of AC, as well as applying practical optimum extraction conditions, 160 g kg-1 extract with an AC ≥ 80 g kg-1 could be consistently achieved from green rooibos plant material. © 2017 Society of Chemical Industry.; © 2017 Society of Chemical Industry.

Moisture sorption isotherm data of ready‐to‐puff preconditioned brown rice shall enable in finding solutions for prolonging the period between preconditioning and puffing. Designed full factorial experiments were conducted with ready‐to‐puff preconditioned brown rice at five different salt concentrations (SC) ranging 0–4%, varying temperature (T), 20–30°C within eight levels of moisture content (MC), and 3–25% to obtain sorption isotherms. Preconditioning was carried out at 75(±3)°C using a fluidized bed dryer to attain a final MC of 11%, optimum for puffing. Water activity (aw) of the sample increased with increasing T and decreased with increasing SC. The individual and interaction effects of T, SC, and MC on aw are highly significant (p

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero‐inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean‐variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase. Publisher PDF

Invited for this month's cover picture is the group of Professor Naoki Saito at the Graduate School of Pharmaceutical Sciences, Meiji Pharmaceutical University (Japan). They achieved the first total synthesis of renieramycin T in 2016, and they have been following an alternative route to supply a large amount of it in order to promote research of the next stage, such as structure–activity relationship studies. This paper reports a formal total synthesis in 21 steps from a known piperazine‐2,5‐dione derivative. The key step of this synthesis is the modified Pictet–Spengler cyclization of a primary amine with an oxomalonic acid ester derivative followed by decarboxylation, and stereo‐controlled protonation at C‐1 position of the enol intermediate from the less‐hindered face. Read the full text of their Full Paper at https://doi.org/10.1002/open.201800112.

In this work, we demonstrate the scale-up from an 80 L fed-batch scale to 40 m(3) along with the design of a 4 m(3) continuous process for enzymatic biodiesel production catalyzed by NS-40116 (a liquid formulation of a modified Thermomyces lanuginosus lipase). Based on the analysis of actual pilot plant data for the transesterification of used cooking oil and brown grease, we propose a method applying first order integral analysis to fed-batch data based on either the bound glycerol or free fatty acid content in the oil. This method greatly simplifies the modeling process and gives an indication of the effect of mixing at the various scales (80 L to 40 m(3) ) along with the prediction of the residence time needed to reach a desired conversion in a CSTR. Suitable process metrics reflecting commercial performance such as the reaction time, enzyme efficiency, and reactor productivity were evaluated for both the fed-batch and CSTR cases. Given similar operating conditions, the CSTR operation on average, has a reaction time which is 1.3 times greater than the fed-batch operation. We also showed how the process metrics can be used to quickly estimate the selling price of the enzyme. Assuming a biodiesel selling price of 0.6 USD/kg and a one-time use of the enzyme (0.1% (w/woil ) enzyme dosage); the enzyme can then be sold for 30 USD/kg which ensures that that the enzyme cost is not more than 5% of the biodiesel revenue. Biotechnol. Bioeng. 2016;113: 1719-1728. © 2016 Wiley Periodicals, Inc.

QSAR/QSPR (quantitative structure‐activity/property relationship) modeling has been a prevalent approach in various, overlapping sub‐fields of computational, medicinal and environmental chemistry for decades. The generation and selection of molecular descriptors is an essential part of this process. In typical QSAR workflows, the starting pool of molecular descriptors is rationalized based on filtering out descriptors which are (i) constant throughout the whole dataset, or (ii) very strongly correlated to another descriptor. While the former is fairly straightforward, the latter involves a level of subjectivity when deciding what exactly is considered to be a strong correlation. Despite that, most QSAR modeling studies do not report on this step. In this study, we examine in detail the effect of various possible descriptor intercorrelation limits on the resulting QSAR models. Statistical comparisons are carried out based on four case studies from contemporary QSAR literature, using a combined methodology based on sum of ranking differences (SRD) and analysis of variance (ANOVA).

This paper proposes an integrated framework for discussing issues related to regional concentration, sectorial specialization and overall localization by considering these concepts as a row-column association– or non-independence– in a two-way contingency table ‘regions × sectors’. This is the approach of stochastic independence, in which the degree of concentration, or of specialization, is measured by discrepancies among distributions: between profiles and a uniform distribution for absolute concepts; between profiles and the corresponding marginal distribution for relative concepts; or between the joint distribution and the product of the marginal distributions for overall localization. This paper discusses the benefits of this integrating approach, particularly for the practitioner facing a multifaceted literature.

The determination of ecological environment damage baseline is the basis of natural resources damage assessment. In complex damage assessment, the importance of baseline is often underestimated or ignored. The existing baseline determination methods have the problems of insufficient accuracy and poor availability in practical application, which affect the damage assessment work to a certain extent. Based on the definition of baseline and the shortcomings of existing baseline determination methods, this paper puts forward the determination principle of the original site point (OSP) method. The baseline calculation area can be directly determined according to the site conditions in the sludge storage site with clear pollution distribution, and the OSP method has certain advantages in the rapidity of determining the baseline. The baseline calculation area should be determined according to the preliminary and detailed sampling data for the waste oil sludge storage site with unclear pollution distribution. The calculation results of the two sites show that the baseline determined by the OSP method and the reference point (RP) method are similar, and the results of the environmental standard (ES) method are much higher than those of the two methods. The order of accuracy of baseline determination methods is the historical data (HD) method > the OSP method > the RP method > the model calculation (MC) method > the ES method. Through two application cases, this paper discusses the applicability of the OSP method, and finally establishes the determination steps of the method. The OSP method is proved to be an effective method to determine the baseline, and the fast and accurate baseline determination method is more helpful to the damage assessment. This article is protected by copyright. All rights reserved.

A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum number of disjoint dicuts in that digraph. In this first paper out of a series of two papers, we conjecture a version of this theorem using a more structural description of this min-max property for finite dicuts in infinite digraphs. We show that this conjecture can be reduced to countable digraphs where the underlying undirected graph is $2$-connected, and we prove several special cases of the conjecture.

In this paper we present a parametric estimation method for certain multi-parameter heavy-tailed Levy-driven moving averages. The theory relies on recent multivariate central limit theorems obtained in [3] via Malliavin calculus on Poisson spaces. Our minimal contrast approach is related to the papers [14, 15], which propose to use the marginal empirical characteristic function to estimate the one-dimensional parameter of the kernel function and the stability index of the driving Levy motion. We extend their work to allow for a multi-parametric framework that in particular includes the important examples of the linear fractional stable motion, the stable Ornstein-Uhlenbeck process, certain CARMA(2, 1) models and Ornstein-Uhlenbeck processes with a periodic component among other models. We present both the consistency and the associated central limit theorem of the minimal contrast estimator. Furthermore, we demonstrate numerical analysis to uncover the finite sample performance of our method.

In a paper from 2001 (Journal of the LMS), Diestel and Leader offered a proof that a connected graph has a normal spanning tree if and only if it does not contain a minor from two specific forbidden classes of graphs, all of cardinality $\aleph_1$. Unfortunately, their proof contains a gap, and their result is incorrect. In this paper, we construct a third type of obstruction: an $\aleph_1$-sized graph without a normal spanning tree that contains neither of the two types described by Diestel and Leader as a minor. Further, we show that any list of forbidden minors characterising the graphs with normal spanning trees must contain graphs of arbitrarily large cardinality., Comment: 9 pages. arXiv admin note: text overlap with arXiv:2005.02833

The purpose of this paper is to extend to ordinal and nominal outcomes the measures of degree of necessity and of sufficiency defined by the authors for dichotomous and survival outcomes in a previous paper. A cause, represented by certain values of prognostic factors, is considered necessary for an event if, without the cause, the event cannot develop. It is considered sufficient for an event if the event is unavoidable in the presence of the cause. The degrees of necessity and sufficiency, ranging from zero to one, are simple, intuitive functions of unconditional and conditional probabilities of an event such as disease or death. These probabilities often will be derived from logistic regression models; the measures, however, do not require any particular model. In addition, we study in detail the relationship between the proposed measures and the related explained variation summary for dichotomous outcomes, which are the common root for the developments for ordinal, nominal, and survival outcomes. We introduce and analyze the Austrian covid-19 data, with the aim of quantifying effects of age and other potentially prognostic factors on covid-19 mortality. This is achieved by standard regression methods but also in terms of the newly proposed measures. It is shown how they complement the toolbox of prognostic factor studies, in particular when comparing the importance of prognostic factors of different types. While the full model's degree of necessity is extremely high (0.933), its low degree of sufficiency (0.179) is responsible for the low proportion of explained variation (0.193).

This paper studies the virtual $\chi_{-y}$-genera of Grothendieck's Quot schemes on surfaces, thus refining the calculations of the virtual Euler characteristics by Oprea-Pandharipande. We first prove a structural result expressing the equivariant virtual $\chi_{-y}$-genera of Quot schemes universally in terms of the Seiberg-Witten invariants. The formula is simpler for curve classes of Seiberg-Witten length $N$, which are defined in the paper. By way of application, we give complete answers in the following cases: (i) arbitrary surfaces for the zero curve class, (ii) relatively minimal elliptic surfaces for rational multiples of the fiber class, (iii) minimal surfaces of general type with $p_g>0$ for any curve classes. Furthermore, a blow up formula is obtained for curve classes of Seiberg-Witten length $N$. As a result of these calculations, we prove that the generating series of the virtual $\chi_{-y}$-genera are given by rational functions for all surfaces with $p_g>0$, addressing a conjecture of Oprea-Pandharipande. In addition, we study the reduced $\chi_{-y}$-genera for $K3$ surfaces and primitive curve classes with connections to the Kawai-Yoshioka formula., Comment: 48 pages. Reformulation of Theorem 1 for readability. Extra explanation for the mixed terms in section 2.2.3. Reference updates

In a paper published in 1939 in The Annals of Mathematical Statistics, Wald and Wolfowitz discussed the possible validity of a probability inequality between one- and two-sided coverage probabilities for the empirical distribution function. Twenty-eight years later, Vandewiele and Noé proved this inequality for Kolmogorov-Smirnov type goodness of fit tests. We refer to this type of inequality as one-two inequality. In this paper, we generalize their result for one- and two-sided union-intersection tests based on positively associated random variables and processes. Thereby, we give a brief review of different notions of positive association and corresponding results. Moreover, we introduce the notion of one-two dependence and discuss relationships with other dependence concepts. While positive association implies one-two dependence, the reverse implication fails. Last but not least, the Bonferroni inequality and the one-two inequality yield lower and upper bounds for two-sided acceptance/rejection probabilities which differ only slightly for significance levels not too large. We discuss several examples where the one-two inequality applies. Finally, we briefly discuss the possible impact of the validity of a one-two inequality on directional error control in multiple testing.

Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE-constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The objective function measures the misfit between the observed data and the calculated synthetic data, and it has traditionally been the least-squares norm. In a sequence of papers, we introduced the Wasserstein metric from optimal transport as an alternative misfit function for mitigating the so-called cycle skipping, which is the trapping of the optimization process in local minima. In this paper, we first give a sharper theorem regarding the convexity of the Wasserstein metric as the objective function. We then focus on two new issues. One is the necessary normalization of turning seismic signals into probability measures such that the theory of optimal transport applies. The other, which is beyond cycle skipping, is the inversion for parameters below reflecting interfaces. For the first, we propose a class of normalizations and prove several favorable properties for this class. For the latter, we demonstrate that FWI using optimal transport can recover geophysical properties from domains where no seismic waves travel through. We finally illustrate these properties by the realistic application of imaging salt inclusions, which has been a significant challenge in exploration geophysics.

In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper., 9 pages. arXiv admin note: text overlap with arXiv:1711.06533

This paper is concerned with voting processes on graphs where each vertex holds one of two different opinions. In particular, we study the \emph{Best-of-two} and the \emph{Best-of-three}. Here at each synchronous and discrete time step, each vertex updates its opinion to match the majority among the opinions of two random neighbors and itself (the Best-of-two) or the opinions of three random neighbors (the Best-of-three). Previous studies have explored these processes on complete graphs and expander graphs, but we understand significantly less about their properties on graphs with more complicated structures. In this paper, we study the Best-of-two and the Best-of-three on the stochastic block model $G(2n,p,q)$, which is a random graph consisting of two distinct Erdős-Renyi graphs $G(n,p)$ joined by random edges with density $q\leq p$. We obtain two main results. First, if $p=\omega(\log n/n)$ and $r=q/p$ is a constant, we show that there is a phase transition in $r$ with threshold $r^*$ (specifically, $r^*=\sqrt{5}-2$ for the Best-of-two, and $r^*=1/7$ for the Best-of-three). If $r>r^*$, the process reaches consensus within $O(\log \log n+\log n/\log (np))$ steps for any initial opinion configuration with a bias of $\Omega(n)$. By contrast, if $r r^*$, we show that, for any initial opinion configuration, the process reaches consensus within $O(\log n)$ steps. To the best of our knowledge, this is the first result concerning multiple-choice voting for arbitrary initial opinion configurations on non-complete graphs.

This paper concerns the existence of transonic shock solutions to the 2-D steady compressible Euler system in an almost flat finite nozzle ( in the sense that it is a generic small perturbation of a flat one ), under physical boundary conditions proposed by Courant-Friedrichs in \cite{CourantFriedrichs1948}, in which the receiver pressure is prescribed at the exit of the nozzle. In the resulting free boundary problem, the location of the shock-front is one of the most desirable information one would like to determine. However, the location of the normal shock-front in a flat nozzle can be anywhere in the nozzle so that it provides little information on the possible location of the shock-front when the nozzle's boundary is perturbed. So one of the key difficulties in looking for transonic shock solutions is to determine the shock-front. To this end, a free boundary problem for the linearized Euler system will be proposed, whose solution will be taken as an initial approximation for the transonic shock solution. In this paper, a sufficient condition in terms of the geometry of the nozzle and the given exit pressure is derived which yields the existence of the solutions to the proposed free boundary problem. Once an initial approximation is obtained, a further nonlinear iteration could be constructed and proved to lead to a transonic shock solution., 53 pages

We establish a theory of $Q$-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\mathrm{mod}(p)$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension., 37 pages. First part of a two-papers work aimed at establishing a first general partial regularity theory for area minimizing currents modulo p, for any p and in any dimension and codimension. v3 is the final version, to appear on Comm. Pure Appl. Math

This paper generalizes the GGP conjectures which were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the nongeneric L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of A-parameters which governs the branching laws for $GL_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in our earlier work including Bessel models and Fourier-Jacobi models., 70 pages, to appear in Compositio Math

The Barat-Thomassen conjecture, recently proved in [Bensmail et al.: A proof of the Barat-Thomassen conjecture. J. Combin. Theory Ser. B, 124:39-55, 2017.], asserts that for every tree T, there is a constant $c_T$ such that every $c_T$-edge connected graph G with number of edges (size) divisible by the size of T admits an edge partition into copies of T (a T-decomposition). In this paper, we investigate in which case the connectivity requirement can be dropped to a minimum degree condition. For instance, it was shown in [Bensmail et al.: Edge-partitioning a graph into paths: beyond the Barat-Thomassen conjecture. arXiv:1507.08208] that when T is a path with k edges, there is a constant $d_k$ such that every 24-edge connected graph G with size divisible by k and minimum degree $d_k$ has a T-decomposition. We show in this paper that when F is a coprime forest (the sizes of its components being a coprime set of integers), any graph G with sufficiently large minimum degree has an F-decomposition provided that the size of F divides the size of G (no connectivity is required). A natural conjecture asked in [Bensmail et al.: Edge-partitioning a graph into paths: beyond the Barat-Thomassen conjecture. arXiv:1507.08208] asserts that for a fixed tree T, any graph G of size divisible by the size of T with sufficiently high minimum degree has a T-decomposition, provided that G is sufficiently highly connected in terms of the maximal degree of T. The case of maximum degree 2 is answered by paths. We provide a counterexample to this conjecture in the case of maximum degree 3.

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.

This paper is a rebuttal to the claim found in the literature that the MUSCL scheme cannot be third-order accurate for nonlinear conservation laws. We provide a rigorous proof for third-order accuracy of the MUSCL scheme based on a careful and detailed truncation error analysis. Throughout the analysis, the distinction between the cell average and the point value will be strictly made for the numerical solution as well as for the target operator. It is shown that the average of the solutions reconstructed at a face by Van Leer's kappa-scheme recovers a cubic solution exactly with kappa = 1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third-order truncation error. Finally, noting that the target spatial operator is a cell-averaged flux derivative, we prove that the leading truncation error of the MUSCL finite-volume scheme is third-order with kappa = 1/3. The importance of the diffusion scheme is also discussed: third-order accuracy will be lost when the third-order MUSLC scheme is used with a wrong fourth-order diffusion scheme for convection-diffusion problems. Third-order accuracy is verified by thorough numerical experiments for both steady and unsteady problems. This paper is intended to serve as a reference to clarify confusions about third-order accuracy of the MUSCL scheme, as a guide to correctly analyze and verify the MUSCL scheme for nonlinear equations, and eventually as the basis for clarifying third-order unstructured-grid schemes in a subsequent paper.

Generalized estimating equations (GEE) are extension of generalized linear models (GLM) widely applied in longitudinal data analysis. GEE are also applied in spatial data analysis using geostatistics methods. In this paper, we advocate application of GEE for spatial lattice data by modeling the spatial working correlation matrix using the Moran's index and the spatial weight matrix. We present theoretical developments and results for simulated and actual data as well. For the former case, 1,000 samples of a random variable (response variable) defined in (0, 1) interval were generated using different values of the Moran's index. In addition, 1,000 samples of a binary and a continuous variable were also randomly generated as covariates. In each sample, three structures of spatial working correlation matrices were used while modeling: The independent, autoregressive, and the Toeplitz structure. Two measures were used to evaluate the performance of each of the spatial working correlation structures: the asymptotic relative efficiency and the working correlation selection criterions. The results showed that both measures indicated that the autoregressive spatial working correlation matrix proposed in this paper presents the best performance in general. For the actual data case, the proportion of small farmers who used improved maize varieties was considered as the response variable and a set of nine variables were used as covariates. Two structures of spatial working correlation matrices were used and the results showed consistence with those obtained in the simulation study.

It is well known that when the geometry and/or coefficients allow stable trapped rays, the solution operator of the Helmholtz equation (a.k.a. the resolvent of the Laplacian) grows exponentially through a sequence of real frequencies tending to infinity. In this paper we show that, even in the presence of the strongest-possible trapping, if a set of frequencies of arbitrarily small measure is excluded, the Helmholtz solution operator grows at most polynomially as the frequency tends to infinity. One significant application of this result is in the convergence analysis of several numerical methods for solving the Helmholtz equation at high frequency that are based on a polynomial-growth assumption on the solution operator (e.g. $hp$-finite elements, $hp$-boundary elements, certain multiscale methods). The result of this paper shows that this assumption holds, even in the presence of the strongest-possible trapping, for most frequencies.

We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area. We also present several recently introduced ideas, including the notion of Haar meager sets, which are closely analogous to Haar null sets. We prove some results in a more general setting than that of the papers where they were originally proved and prove some results for Haar meager sets which were already known for Haar null sets.

In this paper, we show how to use the framework of mod-Gaussian convergence in order to study the fluctuations of certain models of random graphs, of random permutations and of random integer partitions. We prove that, in these three frameworks, a generic homogeneous observable of a generic random model is mod-Gaussian under an appropriate renormalisation. This implies a central limit theorem with an extended zone of normality, a moderate deviation principle, an estimate of the speed of convergence, a local limit theorem and a concentration inequality. The universal asymptotic behavior of the observables of these models gives rise to a notion of mod-Gaussian moduli space., Comment: New version: the paper has been slightly shortened, and a few references were added. 52 pages, 13 figures

Justifying ridge regression from a geometrical perspective is one of the main contributions of this paper. To the best of our knowledge, this question has not been treated previously. This paper shows that ridge regression is a particular case of raising procedures that provide greater flexibility by transforming the matrix X associated with the model. Thus, raising procedures, based on a geometrical idea of the vectorial space associated with the columns of matrix X, lead naturally to ridge regression and justify the presence of the well‐known constant k on the main diagonal of matrix X′X. This paper also analyses and compares different alternatives to raising with respect to collinearity mitigation. The results are illustrated with an empirical application.

The theory of mixed multiplicities of filtrations by $m$-primary ideals in a ring is introduced in a recent paper by Cutkosky, Sarkar and Srinivasan. In this paper, we consider the positivity of mixed multiplicities of filtrations. We show that the mixed multiplicities of filtrations must be nonnegative real numbers and give examples to show that they could be zero or even irrational. When $R$ is analytically irreducible, and $\mathcal I(1),\ldots,\mathcal I(r)$ are filtrations of $R$ by $m_R$-primary ideals, we show that all of the mixed multiplicities $e_R(\mathcal I(1)^{[d_1]},\ldots,\mathcal I(r)^{[d_r]};R)$ are positive if and only if the ordinary multiplicities $e_R(\mathcal I(i);R)$ for $1\le i\le r$ are positive. We extend this to modules and prove a simple characterization of when the mixed multiplicities are positive or zero on a finitely generated module., 15 pages

Odds ratios approximate risk ratios when the outcome under consideration is rare but can diverge substantially from risk ratios when the outcome is common. In this paper, we derive optimal analytic conversions of odds ratios and hazard ratios to risk ratios that are minimax for the bias ratio when outcome probabilities are specified to fall in any fixed interval. The results for hazard ratios are derived under a proportional hazard assumption for the exposure. For outcome probabilities specified to lie in symmetric intervals centered around 0.5, it is shown that the square-root transformation of the odds ratio is the optimal minimax conversion for the risk ratio. General results for any nonsymmetric interval are given both for odds ratio and for hazard ratio conversions. The results are principally useful when odds ratios or hazard ratios are reported in papers, and the reader does not have access to the data or to information about the overall outcome prevalence.

Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.

[EN] In this paper, a novel technique is formed to obtain the solution of a fractional gas dynamics equation. Some reproducing kernel Hilbert spaces are defined. Reproducing kernel functions of these spaces have been found. Some numerical examples are shown to confirm the efficiency of the reproducing kernel Hilbert space method. The accurate pulchritude of the paper is arisen in its strong implementation of Caputo fractional order time derivative on the classical equations with the success of the highly accurate solutions by the series solutions. Reproducing kernel Hilbert space method is actually capable of reducing the size of the numerical work. Numerical results for different particular cases of the equations are given in the numerical section., This research was partially supported by Spanish Ministerio de Ciencia, Innovacion y Universidades PGC2018-095896-B-C22 and Generalitat Valenciana PROMETEO/2016/089.

There are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this paper, we develop a local Whittle likelihood approach based on a general score function, with some special cases of which, the approach applies to more applications. This paper highlights the effective asymptotics of our general local Whittle estimator, and presents a comparison with other estimators. Additionally, for a special case, we construct the one‐step ahead predictor based on the form of the score function. Subsequently, we show that it has a smaller prediction error than the classical exponentially weighted linear predictor. The provided numerical studies show some interesting features of our local Whittle estimator.