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O_LIBirdsong is an important signal in mate attraction and territorial defense. Quantifying the complexity of these songs can shed light on individual fitness, sexual selection, and behavior. Several techniques have been used to quantify song complexity and be broadly categorized into diversity indices, measures of stationary probabilities, and measures of sequential variations. However, these methods are unable to account for important acoustic features like the frequency bandwidth and the variety in the shape of syllables which are an integral part of these vocal signals. This study proposes a new complexity measure that considers intra-song note variability and calculates a weighted index for birdsongs using spectral cross-correlation. C_LIO_LIWe compared the previously described methods to understand the advantages and limitations based on the factors that would be affecting the complexity of songs. We developed a new method- Note Variability Index (NVI), which incorporates the spectral features of notes while quantifying complexity. This measure alleviates the need for manual annotations of notes that can be error-prone. We used Spectrogram Cross-Correlation (SPCC) to compare notes within a song and used the output values to quantify song complexity. C_LIO_LITo check for the efficacy of the new method, we generated synthetic songs to caricature extremes in song complexity and compared selected conventional complexity measures along with the NVI. We provide case-specific limitations of these methods. Additionally, to examine the efficacy of this new method in real-world scenarios, we used natural birdsongs from multiple species across the globe with varying song structures to compare conventional methods with NVI. C_LIO_LITo our knowledge, NVI is the only song complexity method that captures the variation of spectral features of notes in songs where the conventional methods fail to distinguish between similar song structures with different note types. As NVI does not need a manual classification of notes, it can be easily implemented for any type of birdsong with existing sound analysis softwares; it is very quick, avoids the possible biases in note classification, and can possibly be automated for large datasets in the future. C_LI

Let $\Omega\subset\mathbb R^n$ be a $C^1$ domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In this paper it is shown that if $u$ is a function harmonic in $\Omega$ and continuous in $\overline \Omega$ which vanishes in a relatively open subset $\Sigma\subset\partial\Omega$ and moreover the normal derivative $\partial_\nu u$ vanishes in a subset of $\Sigma$ with positive surface measure, then $u$ is identically $0$., Comment: More detailed explanation in some argument involving integration by parts and in Remark 3.3. An additional appendix with a self-contained proof of Lemma 4.3, whose proof was not included in the paper previously

In this paper we generalize an equation studied by Mossino and Temam, to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad, to model the behavior of plasma confined in a toroidal vessel. We prove existence of a $W^{2,p}$-viscosity solution and regularity up to $C^{1,\alpha}(\overline{\Omega})$ for any $\alpha

The result of a meta-analysis is conventionally pictured in the forest plot as a diamond, whose length is the 95% confidence interval (CI) for the summary measure of interest. The Diamond Ratio (DR) is the ratio of the length of the diamond given by a random effects meta-analysis to that given by a fixed effect meta-analysis. The DR is a simple visual indicator of the amount of change caused by moving from a fixed-effect to a random-effects meta-analysis. Increasing values of DR greater than 1.0 indicate increasing heterogeneity relative to the effect variances. We investigate the properties of the DR, and its relationship to four conventional but more complex measures of heterogeneity. We propose for the first time a CI on the DR, and show that it performs well in terms of coverage. We provide example code to calculate the DR and its CI, and to show these in a forest plot. We conclude that the DR is a useful indicator that can assist students and researchers to understand heterogeneity, and to appreciate its extent in particular cases.

Mitigating bias in machine learning is a challenging task, due in large part to the presence of competing objectives. Namely, a fair algorithm often comes at the cost of lower predictive accuracy, and vice versa, a highly predictive algorithm may be one that incurs high bias. This work presents a methodology for estimating the fairness-accuracy Pareto front of a fully-connected feedforward neural network, for any accuracy measure and any fairness measure. Our experiments firstly reveal that for training data already exhibiting disparities, a newly introduced causal notion of fairness may be capable of traversing a greater part of the fairness-accuracy space, relative to more standard measures such as demographic parity and conditional parity. The experiments also reveal that tools from multi-objective optimisation are crucial in efficiently estimating the Pareto front (i.e., by finding more non-dominated points), relative to other sensible but ad-hoc approaches. Finally, the work serves to highlight possible synergy between deep learning and multi-objective optimisation. Given that deep learning is increasingly deployed in real-world decision making, the Pareto front can provide a formal way to reason about inherent conflicts.

In this paper, we study the problem of constructing flat inputs for multi-output dynamical systems, in particular, we address the issue of the minimal modification of the initial dynamical system (the measure of modification being the number of equations that have to be changed by adding flat inputs). We show that in the observable case, control vector fields that distort m equations only (where m is the number of measurements) can always be constructed (and this is the minimal possible number of equations that have to be modified by adding flat inputs), while in the unobservable case, the best that we can hope for is that m + 1 equations only are modified such that they involve flat inputs. We discuss when the original output is a flat output of minimal possible differential weight for the minimally modified control system (where by differential weight, we mean the minimal number of derivatives of components of a flat output needed to express all states and controls). We propose a solution for constructing flat inputs leading to a minimally modified control system consistent with the minimal differential weight and, moreover, for which the observable part is affected by the minimal possible number of controls (this last property being important in applications). We show that, in that case, at least 2m − 1 equations have to be affected by the flat inputs.

Aún no está publicado oficialmente. No se conoce volumen, número ni páginas, sólo el año. We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second-order difference or differential operator. In mathematical physics, they allow the explicit computation of bound states of rational extensions of classical quantum-mechanical potentials. The most apparent difference between classical or classical discrete orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their degrees, in the sense that not all degrees are present in the sequence of polynomials. The new examples have the novelty that they depend on an arbitrary number of continuous parameters.

Resonance Raman optical activity (RROA) is commonly measured as the difference in intensity of Raman scattered right and left circularly polarized light, IR -IL , when a randomly polarized light is in resonance with a chiral molecule. Strong and sometimes mono-signate experimental RROA spectra of several chiral solutes were reported previously, although their signs and relative intensities could not be reproduced theoretically. By examining multiple light-matter interaction events which can occur simultaneously under resonance, we show that a new form of chiral Raman spectroscopy, eCP-Raman, a combination of electronic circular dichroism and circularly polarized Raman, prevails. By incorporating the finite-lifetime approach for resonance, the experimental patterns of the model chiral solutes are captured theoretically by eCP-Raman, without any RROA contribution. The results open opportunity for applications of eCP-Raman spectroscopy and for extracting true RROA experimentally.

The assessment of CASP models for utility in molecular replacement is a measure of their use in a valuable real-world application. In CASP7, the metric for molecular replacement assessment involved full likelihood-based molecular replacement searches; however, this restricted the assessable targets to crystal structures with only one copy of the target in the asymmetric unit, and to those where the search found the correct pose. In CASP10, full molecular replacement searches were replaced by likelihood-based rigid-body refinement of models superimposed on the target using the LGA algorithm, with the metric being the refined log-likelihood-gain (LLG) score. This enabled multi-copy targets and very poor models to be evaluated, but a significant further issue remained: the requirement of diffraction data for assessment. We introduce here the relative-expected-LLG (reLLG), which is independent of diffraction data. This reLLG is also independent of any crystal form, and can be calculated regardless of the source of the target, be it X-ray, NMR or cryo-EM. We calibrate the reLLG against the LLG for targets in CASP14, showing that it is a robust measure of both model and group ranking. Like the LLG, the reLLG shows that accurate coordinate error estimates add substantial value to predicted models. We find that refinement by CASP groups can often convert an inadequate initial model into a successful MR search model. Consistent with findings from others, we show that the AlphaFold2 models are sufficiently good, and reliably so, to surpass other current model generation strategies for attempting molecular replacement phasing.

Time–frequency analysis plays an important role in seismic interpretation and reservoir identification because it reveals the variation of seismic frequency contents over time. The S‐transform is recognized as an efficient method for seismic time–frequency analysis, but its frequency distribution biases the actual Fourier spectrum due to the linear frequency‐dependent term in the analytical window. In this paper, an improved S‐transform, named adaptive parameterized S‐transform, is proposed for identifying delta sandstone reservoirs. In the proposed method, three parameters are introduced into the S‐transform to better adjust the time–frequency resolution in different frequency bands. Then these parameters are selected adaptively by using the concentration measure to provide a highly energy‐concentrated time–frequency representation for seismic signals. Two synthetic examples validate the effectiveness of the proposed method. Analysis of field seismic data illustrates that it can provide a better reservoir interpretation with a high resolution. Comparisons between the wavelet transform, S‐transform, and modified S‐transform prove the superiority of the proposed method in describing reservoir distribution and decreasing the uncertainty of reservoir detection. This paper presents a complementary approach to current methods for reservoir detection and identification.

The distribution of parasites in host populations is integral to simulations of parasite populations.We compared three methods to measure parasite aggregation, namely the Hoover, Coefficient of Variation and I10 indices, using field data from a range of fish parasites. These included anisakid nematodes, trypanorhynch cestodes and polyopisthocotylean monogeneans from 10 previously published studies and one unpublished study.Positive correlations among the three methods were high. Standard errors and estimated biases obtained by bootstrap methods were smallest for the Hoover index. There was no evidence for a bias-variance trade-off.The analyses suggest that the Hoover index is to be preferred as a measure of aggregation although difficulties remain in deriving theoretical and operational definitions of aggregation.

The method of generalized pairwise comparisons (GPC) is a multivariate extension of the well-known non-parametric Wilcoxon-Mann-Whitney test. It allows comparing two groups of observations based on multiple hierarchically ordered endpoints, regardless of the number or type of the latter. The summary measure, "net benefit," quantifies the difference between the probabilities that a random observation from one group is doing better than an observation from the opposite group. The method takes into account the correlations between the endpoints. We have performed a simulation study for the case of two hierarchical endpoints to evaluate the impact of their correlation on the type-I error probability and power of the test based on GPC. The simulations show that the power of the GPC test for the primary endpoint is modified if the secondary endpoint is included in the hierarchical GPC analysis. The change in power depends on the correlation between the endpoints. Interestingly, a decrease in power can occur, regardless of whether there is any marginal treatment effect on the secondary endpoint. It appears that the overall power of the hierarchical GPC procedure depends, in a complex manner, on the entire variance-covariance structure of the set of outcomes. Any additional factors (such as thresholds of clinical relevance, drop out, or censoring scheme) will also affect the power and will have to be taken into account when designing a trial based on the hierarchical GPC procedure.

We consider a class of autonomous Hamiltonian systems subject to small, time-periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is non-zero. We describe a topological method to establish orbits which diffuse in energy for every suitably small perturbation parameter $\varepsilon>0$. The method yields quantitative estimates: (i) The existence of orbits along which the energy drifts by an amount independent of $\varepsilon$. The time required by such orbits to drift is $O(1/\varepsilon)$; (ii) The existence of orbits along which the energy makes chaotic excursions; (iii) Explicit estimates for the Hausdorff dimension of the set of such chaotic orbits; (iv) The existence of orbits along which the time evolution of energy approaches a stopped diffusion process (Brownian motion with drift), as $\varepsilon$ tends to $0$. For each $\varepsilon$ fixed, the set of initial conditions of the orbits that yield the diffusion process has positive Lebesgue measure, and in the limit the measure of these sets approaches zero. Moreover, we can obtain any desired values of the drift and variance for the limiting Brownian motion, for appropriate sets of initial conditions. A key feature of our topological method is that it can be implemented in computer assisted proofs. We give an application to a concrete model of the planar elliptic restricted three-body problem, on the motion of an infinitesimal body relative to the Neptune-Triton system.

Our paper differs from previous literature in two ways: 1.We think in terms of clinical consequences, what benefits patients, what harms patients. Our main message is: using a not logic-respecting efficacy measure can potentially harm patients in a randomized controlled trial (RCT), as we prove analytically, and demonstrate with the OAK blood-based tumor mutational burden (bTMB) study. 2.We follow nature, which mixes effects within each treatment arm. Our secondary message is that following nature to mix within each treatment arm first before calculating any efficacy measure between treatments resolves issues. For example, following natural mixing to prove ratio of time is logic-respecting avoids the issue that weights of efficacy measures are implicit solution to an equation that depends on the unknown prognostic effect. More importantly, coding subgroup mixable estimation (SEM) by mixing within each treatment arm first and then calculating efficacy will make marginal and conditional efficacy agree, for logic-respecting efficacy measures (be it a ratio or a difference), no matter the outcome is continuous, binary, or time-to-event. One does not have to choose between marginal and conditional.

It is widely accepted that the brain, like any other physical system, is subjected to physical constraints that restrict its operation. The brain's metabolic demands are particularly critical for proper neuronal function, but the impact of these constraints continues to remain poorly understood. Detailed single-neuron models are recently integrating metabolic constraints, but these models' computational resources make it challenging to explore the dynamics of extended neural networks, which are governed by such constraints. Thus, there is a need for a simplified neuron model that incorporates metabolic activity and allows us to explore the dynamics of neural networks. This work introduces an energy-dependent leaky integrate-and-fire (EDLIF) neuronal model extension to account for the effects of metabolic constraints on the single-neuron behavior. This simple, energy-dependent model could describe the relationship between the average firing rate and the Adenosine triphosphate (ATP) cost as well as replicate a neuron's behavior under a clinical setting such as amyotrophic lateral sclerosis (ALS). Additionally, EDLIF model showed better performance in predicting real spike trains - in the sense of spike coincidence measure - than the classical leaky integrate-and-fire (LIF) model. The simplicity of the energy-dependent model presented here makes it computationally efficient and, thus, suitable for studying the dynamics of large neural networks.

We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The results are applied to the problem of representing a finitely exchangeable distribution as a mixture of powers, i.e, mixture of distributions of i.i.d. sequences, using a signed mixing measure., 48 pages

Proteins' three-dimensional (3D) structures are analyzed traditionally using geometric descriptors such as torsional angles and inter-atomic distances. In this study a measure that is borrowed from computational geometry, aspect ratio of each tetrahedron in alpha shapes of proteins, is utilized. This geometric descriptor differentiates alpha and beta structural classes of proteins when combined with principal components analysis. The method converts the structures of individual proteins, 3D coordinates of the atoms, to points on a plane. It has a high degree of accuracy in differentiating R and T structures of hemoglobin. Therefore, it is anticipated that the geometric measure can be used successfully in a method that is extended to solve classification problems in machine learning.

In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus explicitly capturing the direct impact of the stressed input factor, as well as indirect effects via other inputs. Furthermore, alternative representations of the cascade sensitivity measure are derived, allowing us to address practical issues, such as incomplete specification of the model and high computational costs. The applicability of the methodology is illustrated through the analysis of a commercially used insurance risk model.

Uncertainty is an irreducible part of predictive science, causing us to over- or underestimate the magnitude of change that a system of interest will face. In a reductionist approach, we may use predictions at the level of individual system components (e.g. species biomass), and combine them to generate predictions for system-level properties (e.g. ecosystem function). Here we show that this process of scaling up uncertain predictions to higher levels of organisation has a surprising consequence: it tends to systematically underestimate the magnitude of system-level change, an effect whose significance grows with the system's dimensionality. This stems from a geometric observation: in high dimensions there are more ways to be more different, than ways to be more similar. We focus on ecosystem-level predictions generated from the combination of predictions at the species level. In this setting, the ecosystem's relevant dimensionality is a measure of its diversity (and not simply the number of species). We explain why dimensional effects do not play out when predicting change of a single linear aggregate property (e.g. total biomass), yet are revealed when predicting change of nonlinear properties (e.g. absolute biomass change, stability or diversity), and when several properties are considered at once to describe the ecosystem, as in multi-functional ecology. As an application we discuss the consequences of our theory for multiple-stressor research. This empirical field focuses on interactions between stressors, defined as the error made by a prediction based on their observed individual effects. Our geometric approach can be visualised and explored with a web application (https://doi.org/10.5281/zenodo.4611133), and we provide pseudocode outlining how our theory can be applied. Our findings highlight and describe the counter-intuitive effects of scaling up uncertain predictions, effects that can occur in any field of science where a reductionist approach is used to generate predictions.

We develop an algorithm for seismic data filtering to preserve the boundary information of faults and other geological bodies while suppressing the noise. Based on the theory of anisotropic diffusion filtering, this method explores the relationship between eigenvalues of the structure tensor and local structural features of three‐dimensional seismic images and innovatively introduces the definition of stratigraphic coherence coefficients. Then we propose a new system to design the eigenvalues of the diffusion tensor by using the fault confidence measure and stratigraphic coherence coefficients, which can control the filtering intensity of seismic data in different orientations. The value of fault confidence measure is close to 0 where there are flat continuous reflectors and the intensity of diffusion is strong. On the contrary, the diffusion is very weak within presumptive fault zones. Results of both synthetic model and real data prove that the proposed method can effectively suppress noise, preserve faults well and enhance the continuity of the reflectors, which can provide basic data with high signal‐to‐noise ratio for subsequent seismic interpretation.

Hidden Markov models (HMMs) that include individual-level random effects have recently been promoted for inferring animal movement behaviour from biotelemetry data. These “mixed HMMs” come at significant cost in terms of implementation and computation, and discrete random effects have been advocated as a practical alternative to more computationally-intensive continuous random effects. However, the performance of mixed HMMs has not yet been sufficiently explored to justify their widespread adoption, and there is currently little guidance for practitioners weighing the costs and benefits of mixed HMMs for a particular research objective.I performed an extensive simulation study comparing the performance of a suite of fixed and random effect models for individual heterogeneity in the hidden state process of a 2-state HMM. I focused on sampling scenarios more typical of telemetry studies, which often consist of relatively long time series (30 – 250 observations per animal) for relatively few individuals (5 – 100 animals).I generally found mixed HMMs did not improve state assignment relative to standard HMMs. Reliable estimation of random effects required larger sample sizes than are often feasible in telemetry studies. Continuous random effect models performed reasonably well with data generated under discrete random effects, but not vice versa. Random effects accounting for unexplained individual variation can improve estimation of state transition probabilities and measurable covariate effects, but discrete random effects can be a relatively poor (and potentially misleading) approximation for continuous variation.When weighing the costs and benefits of mixed HMMs, three important considerations are study objectives, sample size, and model complexity. HMM applications often focus on state assignment with little emphasis on heterogeneity in state transition probabilities, in which case random effects in the hidden state process simply may not be worth the additional effort. However, if explaining variation in state transition probabilities is a primary objective and sufficient explanatory covariates are not available, then random effects are worth pursuing as a more parsimonious alternative to individual fixed effects.To help put my findings in context and illustrate some potential challenges that practitioners may encounter when applying mixed HMMs, I revisit a previous analysis of long-finned pilot whale biotelemetry data.

This paper is about quantitative linearization results for the Monge-Ampere equation with rough data. We develop a large-scale regularity theory and prove that if a measure µ is close to the Lebesgue measure in Wasserstein distance at all scales, then the displacement of the macroscopic optimal coupling is quantitatively close at all scales to the gradient of the solution of the corresponding Poisson equation. The main ingredient we use is a harmonic approximation result for the optimal transport plan between arbitrary measures. This is used in a Campanato iteration which transfers the information through the scales.

The limitations of GDP as a measure of welfare are well known. We propose a new method of estimating the well‐being of nations. Using gross bilateral international migration flows and a discrete choice model in which everyone in the world chooses a country in which to live, we estimate each country's overall quality of life. Our estimates, by relying on revealed preference, complement previous estimates of well‐being that consider only income or a small number of factors, or rely on structural assumptions about how these factors contribute to well‐being.

The categorical Gini correlation is an alternative measure of dependence between a categorical and numerical variables, which characterizes the independence of the variables. A nonparametric test for the equality of K distributions has been developed based on the categorical Gini correlation. By applying the jackknife empirical likelihood approach, the standard limiting chi-square distribution with degree freedom of $K-1$ is established and is used to determine critical value and $p$-value of the test. Simulation studies show that the proposed method is competitive to existing methods in terms of power of the tests in most cases. The proposed method is illustrated in an application on a real data set.

Line-transect distance sampling is widely used to estimate population densities using distances of observed targets from transect lines to model detectability. When the target taxa are high density, the frequent measuring of distances may make the method seem impractical. We present a method that improves the efficiency of distance sampling when the target species occurs at high density. Only a proportion of targets are measured to model the detection function, and the time saved on the survey is then used to cover a longer total length of transect and accrue a larger ‘count only’ sample. This approach can improve the precision of the population density estimate when the cost of measuring the distance to a detected target is more than half the cost of walking to the next target. We find the optimal proportion of distances to measure that minimises the variance of the density estimate for a fixed survey budget. We quantify how much this optimised strategy increases the precision of the density estimate compared with conventional line-transect distance sampling. We then use simulated distance sampling data to test our expressions, and illustrate circumstances under which the optimised approach would be beneficial using distance sampling data on high-density plants. The simulations indicate that the optimised method delivers benefits in precision, but the magnitude of the benefit is lower than predicted from our expressions, which are based on an asymptotic approximation of the variance. We apply an adjustment to the predicted benefit equation to account for this difference, and show that, in all three plant case studies, the optimised approach could improve the precision gained from a distance sampling survey between 20% and 50%. This new approach could broaden the ecological contexts in which distance sampling is applied, to include estimation of densities of abundant taxa where plots are conventionally used. The method may have interesting applications for other survey types, including multispecies surveys or those using cues or signs that occur at high density.

The present article deals with intra-horizon risk in models with jumps. Our general understanding of intra-horizon risk is along the lines of the approach taken in Boudoukh et al. (2004); Rossello (2008); Bhattacharyya et al. (2009); Bakshi and Panayotov (2010); and Leippold and Vasiljevic (2020). In particular, we believe that quantifying market risk by strictly relying on point-in-time measures cannot be deemed a satisfactory approach in general. Instead, we argue that complementing this approach by studying measures of risk that capture the magnitude of losses potentially incurred at any time of a trading horizon is necessary when dealing with (m)any financial position(s). To address this issue, we propose an intra-horizon analogue of the expected shortfall for general profit and loss processes and discuss its key properties. Our intra-horizon expected shortfall is well-defined for (m)any popular class(es) of Levy processes encountered when modeling market dynamics and constitutes a coherent measure of risk, as introduced in Cheridito et al. (2004). On the computational side, we provide a simple method to derive the intra-horizon risk inherent to popular Levy dynamics. Our general technique relies on results for maturity-randomized first-passage probabilities and allows for a derivation of diffusion and single jump risk contributions. These theoretical results are complemented with an empirical analysis, where popular Levy dynamics are calibrated to the S&P 500 index and Brent crude oil data, and an analysis of the resulting intra-horizon risk is presented.

This paper proves the validity of the joint mean-field and classical limit of the quantum $N$-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the Euler-Poisson system has a smooth solution that is rapidly decaying at infinity. One key ingredient in the proof is an inequality from [S. Serfaty, with an appendix of M. Duerinckx arXiv:1803.08345v3 [math.AP]].

Objective The circular structure of values has been verified mostly at a between-person level and on measures of general value preferences. In this manuscript, we argue that it is a simplification that neglected significant aspects of the value structures and distinguish four different types of structures: (a) between-person structure of value traits, (b) within-person structure of value traits, (c) between-person structure of value states, and (d) within-person structure of value states. We argue that the within-person structure of value states addresses the circular structure of values most accurately. Method To compare all four structures, we collected three partially dependent samples (N1 = 449, N2 = 293, N3 = 218) of adults (age 17–57, M = 24). At three time points, separated by 5–7 weeks, respondents completed a questionnaire measure (Portrait Values Questionnaire-Revised [PVQ-RR]) of value preferences (value traits) and reported the importance of values in their everyday actions (value states) for 1 week in an experience sampling study. Results The four types of value structures were stable over time. All four were also consistent with Schwartz's value model to some degree, but at the same time, there were some deviations. Conclusions It is important to distinguish four types of value structures and be aware of their different interpretations that we outlined in this paper.

This paper documents a downward hypothetical bias in the willingness to accept measure for a private good using the Becker‐DeGroot‐Marschak (BDM) method. We first construct a theoretical framework that predicts an upward hypothetical bias for the willingness to pay and a downward hypothetical bias for the willingness to accept measure. Based on a field experiment on livestock trading in China, we compare four experiment treatments, including a hypothetical treatment wherein responses are not consequential, two consequential treatments with probabilistic implementation wherein responses have a 25% or 75% probability of being consequential, and a consequential treatment with full implementation wherein responses are 100% consequential. Consistent with our theoretical predictions, the empirical results show that respondents report significant lower (about 12% lower) values in the hypothetical treatment compared with the consequential treatment with full implementation using the willingness to accept measure. The reported values also increase as the implementation probability increases. Our study contributes to the research on hypothetical bias in the willingness to accept by allowing exogenous changes in the consequential probability.

Studying elliptic measure data problem with strongly nonlinear operator whose growth is described by the means of fully anisotropic $N$-function, we prove the uniqueness for a broad class of measures. In order to provide it, the framework of capacities in fully anisotropic Orlicz-Sobolev spaces is developed and the~capacitary characterization of a~bounded measure is given. Moreover, we give an example of an anisotropic Young function $\Phi$, such that $|\xi|^p \lesssim\Phi(\xi)\lesssim |\xi|^p\log^\alpha(1+|\xi|)$, with arbitrary $p\geq 1$, $\alpha>0$, but so irregularly growing that % we call it essentially fully anisotropic. In fact, the Orlicz--Sobolev--type space generated by $\Phi$ indispensably requires fully anisotropic tools to be handled.

For all $1\leq m\leq n-1$, we investigate the interaction of locally finite measures in $\mathbb{R}^n$ with the family of $m$-dimensional Lipschitz graphs. For instance, we characterize Radon measures $\mu$, which are carried by Lipschitz graphs in the sense that there exist graphs $\Gamma_1,\Gamma_2,\dots$ such that $\mu(\mathbb{R}^n\setminus\bigcup_1^\infty\Gamma_i)=0$, using only countably many evaluations of the measure. This problem in geometric measure theory was classically studied within smaller classes of measures, e.g.~for the restrictions of $m$-dimensional Hausdorff measure $\mathcal{H}^m$ to $E\subseteq \mathbb{R}^n$ with $0, Comment: 18 pages, 1 figure (v2: mostly polishing, updated figure, fixed mistake in proof of Lemma 4.1, added references)

Purpose: In pharmacoepidemiological studies, the precision of effect estimates usually depends on the lowest number in the underlying two by two table. We denote this the “bottleneck count” (BNC). We describe how to translate the BNC into an achievable precision and provide empirical examples. Methods: First, we derive a theoretical prediction of the precision in a study where only the BNC determines precision. As an illustration, we calculated the expected precision of a null-effect study on retinoids and peptic ulcer bleeding, expressed as the upper/lower confidence limit ratio (ULCLR). Finally, we reviewed 126 effect estimates from the literature, analyzing the relationship between the predicted and achieved precision. Results: The log–log transformed ULCLR was shown to be a simple linear function of log(BNC). The expected annual number of retinoid-users experiencing a peptic ulcer bleeding was 9.8, yielding an estimated ULCLR for a 1-year study of 3.84. The literature review showed an inverse linear relationship between the logarithmic BNC and the log–log transformed ULCLR, which was largely independent of study design, effect measure and category of BNC. Achieved precision deviated little from predictions but was usually lower than predicted, particularly with low BNC. Conclusion: The precision of a study can be predicted simply and with good accuracy from the BNC, which is useful for determining whether a study is worth pursuing or not.

1. Resilience is broadly understood as the ability of an ecological system to resist and recover from perturbations acting on species abundances and on the system's structure. However, one of the main problems in assessing resilience is to understand the extent to which measures of recovery and resistance provide complementary information about a system. While recovery from abundance perturbations has a strong tradition under the analysis of dynamical stability, it is unclear whether this same formalism can be used to measure resistance to structural perturbations (e.g., perturbations to model parameters). 2. Here, we provide a framework grounded on dynamical and structural stability in Lotka-Volterra systems to link recovery from small perturbations on species abundances (i.e., dynamical indicators) with resistance to parameter perturbations of any magnitude (i.e., structural indicators). We use theoretical and experimental multispecies systems to show that the faster the recovery from abundance perturbations, the higher the resistance to parameter perturbations. 3. We first use theoretical systems to show that the return rate along the slowest direction after a small random abundance perturbation (what we call full recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). We also show that the return rate along the second fastest direction after a small random abundance perturbation (what we call partial recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before at most one species survives (what we call partial resistance). Then, we use a data set of experimental microbial systems to confirm our theoretical expectations and to demonstrate that full and partial components of resilience are complementary. 4. Our findings reveal that we can obtain the same level of information about resilience by measuring either a dynamical (i.e., recovery) or a structural (i.e., resistance) indicator. Irrespective of the chosen indicator (dynamical or structural), our results show that we can obtain additional information by separating the indicator into its full and partial components. We believe these results can motivate new theoretical approaches and empirical analyzes to increase our understanding about risk in ecological systems.

We study some classical uniqueness and existence results, such as Peano's or Osgood's uniqueness criteria, in the context of Stieltjes differential equations. This type of equation is based on derivatives with respect to monotone functions, and enables the investigation of discrete and continuous problems from a common standpoint. We compare our results with previous work on the topic and illustrate the advantages of the theorems presented in this paper with an example. Finally, we make some remarks regarding analogous uniqueness results which can be derived for measure differential equations.

We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes, providing a bifurcation-type result. Specifically, it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, distorted measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. A byproduct of our work are some new results on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.

We study a class of nonlinear elliptic equations involving measure data −divA(x,Du)=μinΩ,where μ is a Radon measure. Under the main assumption of A(x,ξ) that there exists a constant Λ>0 such that |A(x,ξ)−A(x0,ξ)|≤Λ(a(x)+a(x0))|x−x0|α(|ξ|2+s2)p−12,α∈(0,1],where 0≤a(x)∈Lm(Ω) for some integrable index m>1, we obtain the Calderon–Zygmund estimates in the Sobolev–Morrey spaces for refined fractional‐order derivatives of distributional solutions depending on α.

Consider the Coulomb potential $-\mu\ast|x|^{-1}$ generated by a non-negative finite measure $\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\"odinger operator $-\Delta/2-\mu\ast|x|^{-1}$ is minimized, at fixed mass $\mu(\mathbb{R}^3)=\nu$, when $\mu$ is proportional to a delta. In this paper we investigate the conjecture that the same holds for the Dirac operator $-i\alpha\cdot\nabla+\beta-\mu\ast|x|^{-1}$. In a previous work on the subject we proved that this operator is self-adjoint when $\mu$ has no atom of mass larger than or equal to 1, and that its eigenvalues are given by min-max formulas. Here we consider the critical mass $\nu_1$, below which the lowest eigenvalue does not dive into the lower continuum spectrum for all $\mu\geq0$ with $\mu(\mathbb{R}^3), Comment: Final version to appear in Proc. London Math. Soc

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

We investigate the flattening Phillips relation by making two departures from standard specifications. First, we measure slack using real activity variables that are bandpass filtered or year‐over‐year changes in activity (these are similar), instead of gaps. Second, we study the components of inflation instead of the standard aggregates. We find that some inflation components have strong and stable correlations with the cyclical component of real activity; these components tend to be relatively well‐measured and domestically determined. Other components, typically prices that are poorly measured or internationally determined, have weak and/or unstable correlations with cyclical activity. We construct a new inflation index, cyclically sensitive inflation, that weights the components by their joint cyclical covariation with real activity. The index has strong and stable correlations with cyclical activity and provides a real‐time measure of cyclical movements in inflation.

The Q-matrix identifies the subset of attributes measured by each item in the cognitive diagnosis modelling framework. Usually constructed by domain experts, the Q-matrix might contain some misspecifications, disrupting classification accuracy. Empirical Q-matrix validation methods such as the general discrimination index (GDI) and Wald have shown promising results in addressing this problem. However, a cut-off point is used in both methods, which might be suboptimal. To address this limitation, the Hull method is proposed and evaluated in the present study. This method aims to find the optimal balance between fit and parsimony, and it is flexible enough to be used either with a measure of item discrimination (the proportion of variance accounted for, PVAF) or a coefficient of determination (pseudo-R2 ). Results from a simulation study showed that the Hull method consistently showed the best performance and shortest computation time, especially when used with the PVAF. The Wald method also performed very well overall, while the GDI method obtained poor results when the number of attributes was high. The absence of a cut-off point provides greater flexibility to the Hull method, and it places it as a comprehensive solution to the Q-matrix specification problem in applied settings. This proposal is illustrated using real data.

As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic hypersurfaces meeting a given convex body K is minimized when K is a geodesic ball. We present a random extension of this result by taking K to be the convex hull of finitely many points drawn according to a probability distribution and by showing that the minimum is attained for uniform distributions on geodesic balls. As a corollary, we obtain a randomized Blaschke--Santalo inequality on the sphere.

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and state filters for each mode, our algorithm relies on the ability to find the most probable model as a mode estimate, which we show is possible with input and state filters by identifying a key property, that a particular residual signal we call generalized innovation is a Gaussian white noise. We also provide an asymptotic analysis for the proposed algorithm and provide sufficient conditions for asymptotically achieving convergence to the true model (consistency), or to the 'closest' model according to an information-theoretic measure (convergence). A simulation example of intention-aware vehicles at an intersection is given to demonstrate the effectiveness of our approach., Comment: Submitted to SIAM Journal on Control and Optimization

We used robust skewness measures to revisit a recent theory that the average asymmetry (measured by the average monthly skewness values across firms) can negatively predict future market returns. Skewness measures employed in previous studies are moment‐based which are normally sensitive to outliers of returns. We thus consider a quantile‐based robust skewness measure and find that the predictive power of the average skewness to market returns no longer exists. Instead, we find a negative relation between the average expected (or ex‐ante) skewness and market returns, suggesting that investors’ average expectation on skewness can negatively predict market returns.

We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival data set as well as the linked Surveillance, Epidemiology and End Results (SEER)-Medicare database for prediction of mortality in early-stage prostate cancer patients using high dimensional claims codes., 20 pages, 11 figures

We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total variation, but it characterizes independence (zero Gini correlation mutually implies independence). Closely related to the distance correlation, the Gini correlation is of simple formulation by considering the nature of categorical variable. As a result, the proposed Gini correlation has a lower computational cost than the distance correlation and is more straightforward to perform inference. Simulation and real applications are conducted to demonstrate the advantages., 24 + 3 Pages, 4 figures

Discrete‐time models with periodic behavior are useful for the description of different phenomenon. The most popular time series taking into consideration the periodicity of the real data is the periodic autoregressive moving average (PARMA) model. The PARMA models were considered in the literature from a theoretical and practical point of view. Most of the considerations related to the PARMA models are based on the assumption of the Gaussian (or finite‐variance) distribution of the noise. However, in many applications, the Gaussian distribution seems to be inappropriate. Thus, generalized models are considered. The natural extension of the Gaussian distribution is the α‐stable one which is a perfect distribution for the modeling of real data with large observations. However, for the α‐stable‐based models the classical methods adequate to Gaussian‐based systems cannot be used. The main problem comes from the fact that, in general, for the α‐stable based models the covariance cannot be applied as a measure of dependence. Thus, alternative measures are used. In this article, we consider the generalization of the classical PARMA models and take into consideration the α‐stable PAR system. Moreover, we analyze the bidimensional version of the univariate model and examine its structure of cross‐dependence in the language of the alternative cross‐dependence measures appropriate for the infinite‐variance systems. As the main result, we prove that the ratio of two considered alternative cross‐dependence measures tends to the stability index of the noise distribution. This result is the continuation of the authors' previous research where a similar study was performed for one‐dimensional models based on the α‐stable distribution. Moreover, in the authors' recent papers the stationary bidimensional time series models were considered in the same direction. Finally, we propose a possible application of the introduced methodology.

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.

Let X1,X2,… be independent and identically distributed random elements taking values in a separable Hilbert space ℍ. With applications for functional data in mind, ℍ may be regarded as a space of square‐integrable functions, defined on a compact interval. We propose and study a novel test of the hypothesis H0 that X1 has some unspecified nondegenerate Gaussian distribution. The test statistic Tn = Tn(X1,…,Xn) is based on a measure of deviation between the empirical characteristic functional of X1,…,Xn and the characteristic functional of a suitable Gaussian random element of ℍ. We derive the asymptotic distribution of Tn as n→∞ under H0 and provide a consistent bootstrap approximation thereof. Moreover, we obtain an almost sure limit of Tn and the limit distributions of Tn under fixed and contiguous alternatives to Gaussianity. Simulations show that the new test is competitive with respect to the hitherto few competitors available.

Understanding how stressors combine to affect population abundances and trajectories is a fundamental ecological problem with increasingly important implications worldwide. Generalisations about interactions among stressors are challenging due to different categorisation methods and how stressors vary across species and systems. Here, we propose using a newly introduced framework to analyse data from the last 25 years on ecological stressor interactions, for example combined effects of temperature, salinity and nutrients on population survival and growth. We contrast our results with the most commonly used existing method - analysis of variance (ANOVA) - and show that ANOVA assumptions are often violated and have inherent limitations for detecting interactions. Moreover, we argue that rescaling - examining relative rather than absolute responses - is critical for ensuring that any interaction measure is independent of the strength of single-stressor effects. In contrast, non-rescaled measures - like ANOVA - find fewer interactions when single-stressor effects are weak. After re-examining 840 two-stressor combinations, we conclude that antagonism and additivity are the most frequent interaction types, in strong contrast to previous reports that synergy dominates yet supportive of more recent studies that find more antagonism. Consequently, measuring and re-assessing the frequency of stressor interaction types is imperative for a better understanding of how stressors affect populations.

Fuzziness in a fuzzy set is determined by its membership function (m.f) which translates the reality of a problem. Accordingly, the shapes of membership functions (m.fs) are important for a particular problem such as poverty since they effect on a fuzzy inference system. Some authors have used to visualize the behaviour of poverty, different shapes like triangular, trapezoidal. In this paper, a specific (m.f), named modified logistic membership function better illustrating the complicated reality, is proposed to measure poverty. The modified logistic membership function is first formulated for several states of poverty and its flexibility in taking up vagueness in poverty is established by an analytical approach using aggregate operators in order to infer a logical conclusion measuring poverty. An application based on individual well‐being data from Tunisian households in 2010 is presented to illustrate use of proposed concepts.