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This discussion reviews the paper by Zhengjun Zhang in the context of broader research on multivariate extreme value theory and max-stable processes.

Let me start by acknowledging Dr Jun Shao's (the Editor of the journal) invitation to participate in the discussion of the exciting review paper, and congratulations to Dr Yichun Chi and Dr Jun Cai...

The purpose of this note is to discuss how paper folding can be used to find the exact trigonometric ratios of the following four angles: 22.5°, 67.5°, 27°, and 63°.

I commend Drs. Prentice and Huang (PH) for their continued and longstanding commitment to the generation of knowledge concerning the nutritional causes of chronic diseases, and in their dedication ...

I would like to take this opportunity to congratulate Zhengjun for his continuing contribution to extreme-value statistics in recent years. In this review paper, some fundamental theories on univar...

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown.

Numerical simulation of deterministic freak wave sequences and wave-structure interactionThe objective of this study is to propose a new method to generate deterministic freak wave sequences in num...

In the article ‘How long is my toilet roll-a simple exercise in mathematical modelling’ several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a laboratory is an important part of the experiment. The calculation of the absolute errors in indirect measurements provides us with information about the confidence that we must have in our experimental results. For that reason, the error calculation for all approximations has been made

The purpose of this short paper is to describe a new proof of the Pythagorean Theorem that involves paper folding.

This short paper characterizes strictly convex sets by the uniqueness of support points (such points are called unique support points or exposed points) under appropriate assumptions. A class of so...

Viewing from polynomials solutions of q-difference equations makes certain generating functions calculated easily. In this short paper, we build the relations between Cigler’s polynomials and q-difference equations. In addition, we deduce generating functions and bilinear generating functions for Cigler’s polynomials. More over, we gain multilinear and mixed generating functions for Cigler’s polynomials. At last, we gain U(n+1) type generating functions for Cigler’s polynomials.

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.

The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

“with Cryptography” and “Lawrence Washington”11Washington and Wade Trappe are authors of a standard cryptography textbook, Introduction to Cryptography with Coding Theory. are the prompts for this ...

This paper presents interval estimation for the population mean and coefficient of variation in a two-parameter exponential distribution. The new generalized pivot, profile likelihood function and likelihood ratio statistic are derived and used to construct the confidence intervals. A highlight of this paper is that the generalized and likelihood ratio confidence intervals for the mean and coefficient of variation perform well in terms of coverage probability in many cases. Finally, two real-data applications on the air pollution of particulate matter (PM2.5) and the renewable energy through wind power of Thailand are used for illustration purposes.

In a previous paper, we introduced the Collatz polynomials $P_N(z)$, whose coefficients are the terms of the Collatz sequence of the positive integer $N$. Our work in this paper expands on our previous results, using the Enestr\"om-Kakeya Theorem to tighten our old bounds of the roots of $P_N(z)$ and giving precise conditions under which these new bounds are sharp. In particular, we confirm an experimental result that zeros on the circle $\{z\in\mathbb{C}: |z| = 2\}$ are rare: the set of $N$ such that $P_N(z)$ has a root of modulus 2 is sparse in the natural numbers. We close with some questions for further study., Comment: 8 pages, 1 figure

Online experiments are the gold standard for evaluating impact on user experience and accelerating innovation in software. However, since experiments are typically limited in duration, observed treatment effects are not always permanently stable, sometimes revealing increasing or decreasing patterns over time. There are multiple causes for a treatment effect to change over time. In this paper, we focus on a particular cause, user-learning, which is primarily associated with novelty or primacy. Novelty describes the desire to use new technology that tends to diminish over time. Primacy describes the growing engagement with technology as a result of adoption of the innovation. User-learning estimation is critical because it holds experimentation responsible for trustworthiness, empowers organizations to make better decisions by providing a long-term view of expected impact, and prevents user dissatisfaction. In this paper, we propose an observational approach, based on difference-in-differences technique to estimate user-learning at scale. We use this approach to test and estimate user-learning in many experiments at Microsoft. We compare our approach with the existing experimental method to show its benefits in terms of ease of use and higher statistical power, and to discuss its limitation in presence of other forms of treatment interaction with time., Submitted to the Technometrics Journal

Real-world route navigation data indicate that nontrivial portion of drivers do not prefer the system-recommended best routes. Current navigation systems have simplified assumptions about drivers’ route choice preferences and do not adequately accommodate drivers’ heterogeneous route choice preferences, mainly because of: (i) difficulty in acquiring exogenous criteria (e.g., sociodemographic information) that are typically used to differentiate drivers’ preferences in behavioral modeling; and (ii) difficulty in capturing preference of individuals due to limited preference data at the individual level. To address these, this paper introduced a human-centric machine learning technique named Multi-Task Linear Classification Model Adaption (MT-LinAdapt). It can capture drivers’ common aspects of route choice preferences and yet adapts to each driver’s own preference. In addition, any evolvement of individual drivers’ preferences can be simultaneously integrated to update the common preference for further individual drivers’ preference adaptation. This paper evaluated MT-LinAdapt against two state-of-the-art route recommendation strategies including an aggregate-level and an individual-level data-based strategies, which are categorized based on the data used for modeling. With a real-world dataset containing 30,837 drivers’ navigation usage data in Daegu City, South Korea, MT-LinAdapt was compared to existing strategies for its performance at different levels of data availability, and showed at least the same performance with existing strategies when minimum preference data is available and achieves up to 7% higher prediction accuracy as more data becomes available. Higher prediction accuracies are expected to bring better user satisfaction and compliance rates which can further help with transportation system control and management strategies.

Atherosclerosis is a leading cause of death worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. The pathophysiology of diabetic vascular disease is generally understood. Dyslipidemia with increased levels of atherogenic LDL, hyperglycemia, oxidative stress and increased inflammation are factors that increase the risk and accelerate development of atherosclerosis. In a recent paper [53], we have developed mathematical model that includes the effect of hyperglycemia and insulin resistance on plaque growth. In this paper, we propose a more comprehensive mathematical model for diabetic atherosclerosis which include more variables; in particular it includes the variable for Advanced Glycation End-Products (AGEs)concentration. Hyperglycemia trigger vascular damage by forming AGEs, which are not easily metabolized and may accelerate the progression of vascular disease in diabetic patients. The model is given by a system of partial differential equations with a free boundary. We also establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

In recent years, the wide use of deep learning based methods has greatly improved the classification performance of hyperspectral image (HSI). As an effective method to improve the performance of deep convolution networks, attention mechanism is also widely used for HSI classification tasks. However, the majority of the existing attention mechanisms for HSI classification are based on the convolution layer, and the classification accuracy still has margins for improvement. Motivated by the latest self attention mechanism in natural language processing, a deep transformer is proposed for HSI classification in this paper. Specifically, deep transformer along the spectral dimension and the spatial dimension are explored respectively. Then, a deep spatial-spectral transformer (DSS-TRM) is proposed to improve the classification performance of HSI. The contribution of this paper is to make full use of self attention mechanism, that is to use transformer layer instead of convolution layer. More importantly, a DSS-TRM is proposed to realize end-to-end HSI classification. Extensive experiments are conducted on three HSI data sets. The experimental results demonstrates that the proposed DSS-TRM could outperform the traditional convolutional neural networks and attention based methods.

In this paper, solutions of one-phase inverse Stefan problems are studied. The approach presented in the paper is an application of the heat polynomials method (HPM) for solving one- and two-dimens...

In this paper, we construct two families of new explicit exact traveling wave solutions of the Camassa–Holm equation which solve an open problem in the previous paper [Zhang G, Qiao ZJ, Liu F. Cusp...

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled ‘Project Maths’ (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. https://www.education.ie/en/Publications/Policy-Reports/Report-of-the-Project-Maths-Implementation-Group.pdf]. This paper aims to examine the performance of 1st year undergraduate students’ procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students’ skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the ‘why’ of the results presented here.

The dramatic changes brought on by the COVID-19 pandemic have changed the way in which mathematics and statistics support is offered. Students and staff have been presented with new opportunities and challenges. One-on-one interviews were conducted late in 2020 with 23 students and staff who had experience with fully online mathematics and statistics support. The interviewees were from University College Dublin, Ireland, and Western Sydney University, Australia. Utilising thematic analysis, five themes around online mathematics and statistics support common to both universities were identified. In this paper the three themes related to connection are explored;they are pedagogical changes, social interaction, and appreciation of mathematics and statistics support. These themes highlight the need felt by both students and staff for mutual connection. The paper concludes with a discussion on the repercussions of this study for future considerations of effective online mathematics and statistics support. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature that the conventional SUR estimator, for example, the generalized least squares (GLS) estimator of Zellner (1962) does not perform well. As the main contribution of the paper, we propose a new feasible GLS estimator called the feasible graphical lasso (FGLasso) estimator. For a feasible implementation of the GLS estimator, we use the graphical lasso estimation of the precision matrix (the inverse of the covariance matrix of the equation system errors) assuming that the underlying unknown precision matrix is sparse. We derive asymptotic theories of the new estimator and investigate its finite sample properties via Monte-Carlo simulations.

The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to the multigroup neutron diffusion equation and demonstrates its benefits over the conventional straight-sided VEM for a number of benchmark verification test cases with curvilinear domains. These domains were constructed using a topological data-structure developed as part of this paper, based on the doubly-connected edge list, with curves and surfaces both represented using non-uniform rational B-splines (NURBS). This data-structure is used both to specify the geometry of the reactor and to represent the curvilinear polygonal mesh. We also present two separate methods of performing integrations on curvilinear polygons, one for homogeneous functions and one for non-homogeneous functions.

In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the drift term, and is weakly elliptic. The outcome of the paper is twofold. One one hand, we provide Lipschitz regularity results for weakly elliptic non-local HJB, extending the results previously obtained in [8]. On the other hand, we establish a convergence result, based on half relaxed limits and a comparison principle for the effective problem. The latter strongly relies on the regularity and the ellipticity properties of the effective Hamiltonian, for which a fine Lipschitz estimate of the corrector plays a crucial role.

This paper presents a methodological update to the World Bank's toolkit for small area estimation. The paper reviews the computational procedures of the current methods used by the institution: the traditional ELL approach and the Empirical Best (EB) addition introduced to imitate the original EB procedure of Molina and Rao [Small area estimation of poverty indicators. Canadian J Stat. 2010;38(3):369–385], including heteroskedasticity and survey weights, but using a different bootstrap approach, here referred to as clustered bootstrap. Simulation experiments provide empirical evidence of the shortcomings of the clustered bootstrap approach, which yields biased and noisier point estimates. The document presents an update to the World Bank’s EB implementation by considering the original EB procedures for point and noise estimation, extended for complex designs and heteroscedasticity. Simulation experiments illustrate that the revised methods yield considerably less biased and more efficient estimators than those obtained from the clustered bootstrap approach.

In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this paper. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.

This paper concerns noncooperative difference games with infinite horizon discounted payoffs. More precisely, it is a sequel to a previous paper [A. Fonseca-Morales and O. Hern'andez-Lerma, Potenti...

This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [9]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than $\pi$. We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in [9] as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not $\pi$ when the conductive transmission eigenfunctions satisfy certain Herglotz functions approximation properties. That means, as long as the corner singularity is not degenerate, the vanishing property holds if the underlying conductive transmission eigenfunctions can be approximated by a sequence of Herglotz functions under mild approximation rates. Third, the regularity requirements on the interior transmission eigenfunctions in [9] are significantly relaxed in the present study for the conductive transmission eigenfunctions. Finally, as an interesting and practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter.

This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations. The paper starts briefly reviewing classical univ...

Contributions of the present paper consist of two parts. In the first one, we contribute to the theory of stochastic calculus for signed measures. For instance, we provide some results permitting to characterize martingales and Brownian motion both defined under a signed measure. We also prove that the uniformly integrable martingales (defined with respect to a signed measure) can be expressed as relative martingales and we provide some new results to the study of the class $\Sigma(H)$ which appeared for the first time in \cite{f} and studied in \cite{f,e,o}. The second part is devoted to the construction of solutions for the \textbf{homogeneous skew Brownian motion equation} and for the \textbf{inhomogeneous skew Brownian motion equation}. To do this, our ingredients are the techniques and results developed in the first part that we apply on some stochastic processes borrowed from the theory of stochastic calculus for signed measures. Our methods are inspired by those used by Bouhadou and Ouknine in \cite{siam}. Moreover, their solution of the inhomogeneous skew Brownian motion equation is a particular case of those we propose in this paper., Comment: 28 pages

This paper considers the local stability problem and estimates the region of attraction (RA) of the positive equilibrium of Lotka-Volterra (L-V) competitive system with time-delays. Based on the stability theory and the quadratic system theory, by choosing some less conservative integral inequalities and appropriate Lyapunov-Krasovskii (L-K) functional, a local stability condition is obtained by means of linear matrix inequalities (LMI) and the estimate of RA of the positive equilibrium is first discussed. Furthermore, the corresponding optimization problem for the estimate of RA is given. Numerical simulations show that the proposed stability condition in this paper is less conservative as compared with the most existing ones and the method of estimating RA is effective.

Peer-Assisted Learning (PAL) schemes typically involve student volunteers (PAL Leaders) designing and delivering sessions that support groups of students in lower years with their studies. This paper discusses three different PAL schemes, within Mathematics degrees at Sheffield Hallam University (a Post-92 University) and The University of York (a Russell Group University), which took place entirely remotely during the Covid-19 pandemic. In this paper, we explore the challenges and benefits of remote PAL schemes via the three case studies, from both staff and student perspectives. There are aspects of PAL in a pandemic that we would (or would not) take forward to a blended or in-person approach in the future. In particular, we found that, while students and staff alike are looking forward to in-person contact to provide them with interactions and easier methods of communication, the remote provision for peer support has real value in terms of accessibility and inclusivity. Furthermore, integrating technology enhanced learning into in-person sessions can provide added value.

The Beale Papers is an 1885 pamphlet in which there are three ciphers, said to contain the location of a hidden treasure. In this paper the ciphers are viewed through Benford’s Law. Statistical ana...

In this paper, the local and global dynamics of a two-stage Bertrand dynamic duopoly model with R&D spillover are studied. This paper aims to study the complex dynamics of the built model by changi...