Rigorous Results Research Articles

Best Practice Guidelines for Propensity Score Methods in Medical Research: Consideration on Theory, Implementation, and Reporting. A Review

AbstractRigorous and reproducible methodology of controlling for bias is essential for high-quality, evidence-based studies. Propensity score matching (PSM) is a valuable way to control for bias and achieve pseudo-randomization in retrospective observation studies. The purpose of this review is to 1) provide a clear conceptual framework for PSM, 2) recommend how to best report its use in studies, and 3) offer some practical examples of implementation. First, this article covers the concepts behind PSM, discusses its pros and cons, and compares it with other methods of controlling for bias, namely, hard/exact matching and regression analysis. Second, recommendations are given for what to report in a manuscript when PSM is used. Finally, a worked example is provided, which can also serve as a template for the reader’s own studies. A study’s conclusions are only as strong as its methods. PSM is an invaluable tool for producing rigorous and reproducible results in observational studies. The goal of this article is to give practicing clinical physicians not only a better understanding of PSM and its implications but the ability to implement it for their own studies. Study DesignReview.

A systematic literature review of community disaster resilience: main and related research areas and agendas

PurposeThis study aims to characterize the main research areas of published works, identify the disciplines that associated with the works and propose research agendas for future inquiries, based on a systematic literature review that encompasses 89 research papers from 2010 to 2020.Design/methodology/approachThis review commenced with the definition of the three research questions, and subsequently three steps were followed: (1) defining criteria for research paper selection; (2) specifying the data bases and selecting the papers based on the criteria and (3) data analysis, conclusion and discussion of selected papers. The search was limited to the selection of research papers in English, focusing on “community disaster resilience” which is the subject of this review and referred to as keywords which were used for the online search for papers. All these three words must be present in the title of the selected papers.FindingsThe area “resilience management” and “disaster resilience assessment” accounted for 43% of the studies, and it indicates that research has emphasized the description of how community disaster resilience has been managed and assessed. Three disciplines relating to disaster resilience are disaster risk science, public health and environment, and it indicates that research has fostered core areas of community disaster resilience. Three key research agenda include a growing trend to describe successful efforts to avert a potentially catastrophic disaster through solution-based case studies; a paradigmatic shift and implementation of how communities could help the disaster victims recuperate from disasters.Research limitations/implicationsThis review is limited to the numbers of chosen papers, as only full papers were chosen. However, in order to establish more rigorous and inclusive results of the study, the numbers of citations of published papers to be chosen for future inquiry should be taken into account.Originality/valueThis present review originally investigated how the concept of disaster resilience has been applied at the community level and in related areas. As resilience is a multidisciplinary concept that has been investigated by several different disciplines, such as sustainability, psychology, economy and sociology, this study looked into how disciplines related to community disaster resilience to provide agenda for future inquiries. This study therefore characterized the main research areas of published works, identified the disciplines that associated with the works and proposed a research agenda for future inquiries.

Urinary proteomics combined with home blood pressure telemonitoring for health care reform trial: rational and protocol

Background Hypertension and diabetes cause chronic kidney disease (CKD) and diastolic left ventricular dysfunction (DVD) as forerunners of disability and death. Home blood pressure telemonitoring (HTM) and urinary peptidomic profiling (UPP) are technologies enabling prevention. Methods UPRIGHT-HTM (Urinary Proteomics Combined with Home Blood Pressure Telemonitoring for Health Care Reform [NCT04299529]) is an investigator-initiated 5-year clinical trial with patient-centred design, which will randomise 1148 patients to be recruited in Europe, sub-Saharan Africa and South America. During the whole study, HTM data will be collected and freely accessible for patients and caregivers. The UPP, measured at enrolment only, will be communicated early during follow-up to 50% of patients and their caregivers (intervention), but only at trial closure in 50% (control). The hypothesis is that early knowledge of the UPP risk profile will lead to more rigorous risk factor management and result in benefit. Eligible patients, aged 55–75 years old, are asymptomatic, but have ≥5 CKD- or DVD-related risk factors, preferably including hypertension, type-2 diabetes, or both. The primary endpoint is a composite of new-onset intermediate and hard cardiovascular and renal outcomes. Demonstrating that combining UPP with HTM is feasible in a multicultural context and defining the molecular signatures of early CKD and DVD are secondary endpoints. Expected outcomes The expected outcome is that application of UPP on top of HTM will be superior to HTM alone in the prevention of CKD and DVD and associated complications and that UPP allows shifting emphasis from treating to preventing disease, thereby empowering patients.

Uniformly Positive Correlations in the Dimer Model and Macroscopic Interacting Self‐Avoiding Walk in ℤd, d ≥ 3

AbstractOur first main result is that correlations between monomers in the dimer model in do not decay to 0 when . This is the first rigorous result about correlations in the dimer model in dimensions greater than 2 and shows that the model behaves drastically differently than in two dimensions, in which case it is integrable and correlations are known to decay to zero polynomially. Such a result is implied by our more general, second main result, which states the occurrence of a phase transition in the model of lattice permutations, which is related to the quantum Bose gas. More precisely, we consider a self‐avoiding walk interacting with lattice permutations and we prove that, in the regime of fully packed loops, such a walk is ‘long’ and the distance between its endpoints grows linearly with the diameter of the box. These results follow from the derivation of a version of the infrared bound from a new general probabilistic settings, with coloured loops and walks interacting at sites and walks entering into the system from some ‘virtual’ vertices. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

Classical solvability to the initial boundary value problem for a forced foam drainage equation

In this paper we study a nonlinear partial differential equation describing the evolution of a forced foam drainage in one dimensional case. A foam drainage equation was proposed by Goldfarb et al. [5] in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Mathematical studies on a foam drainage equation so far are restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. This paper is aimed at proving that the initial boundary value problem for the forced foam drainage equation admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle and comparison theorem. Moreover, the existence of its steady solution and its stability are shown. This is the first rigorous mathematical result for a series of researches on this equation.

Completely Hazy and Transparent Films by Embedding Air Gaps for Elimination of Angular Color Shift in Organic Light-Emitting Diodes.

Red, green, and blue top-emission organic light-emitting diodes (RGB TOLEDs) suffer from white color change with viewing angle due to the microcavity effect, called white angular dependence (WAD). Great efforts are devoted by applying various kinds of hazy films, but they suffer from poor mechanical stability and optical transmittance. Herein, we introduce an air-gap-embedded hazy film (AEHF) to solve these problems and suppress WAD in RGB TOLEDs. The AEHF is designed with optical simulation to realize high haze with transparency. By tuning geometries of the air gap inside the polymer, the AEHF realizes high haze of more than 90% in all RGB colors while maintaining high transparency. To experimentally demonstrate the AEHF, the O2 plasma is treated on a polymer film with AgCl as an etching mask to fabricate microstructures with high aspect ratios. Afterward, PDMS is coated on the patterned surface; air gaps develop spontaneously in the valleys between microstructures during the coating process. Using these processes, an air gap with 1.2 μm size and 400 nm period is formed inside the film and ∼100% haze is achieved while maintaining a high transmittance of 88%; these results agree well with rigorous coupled wave analysis results. By utilizing the AEHF into TOLEDs, the WAD can be drastically suppressed by 95.2% compared with that of a device without AEHF.

Uniform error estimates for artificial neural network approximations for heat equations

Abstract Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly rather high-dimensional partial differential equations (PDEs). Very recently, there have also been a number of rigorous mathematical results in the scientific literature, which examine the approximation capabilities of such deep learning-based approximation algorithms for PDEs. These mathematical results from the scientific literature prove in part that algorithms based on ANNs are capable of overcoming the curse of dimensionality in the numerical approximation of high-dimensional PDEs. In these mathematical results from the scientific literature, usually the error between the solution of the PDE and the approximating ANN is measured in the $L^p$-sense, with respect to some $p \in [1,\infty )$ and some probability measure. In many applications it is, however, also important to control the error in a uniform $L^\infty $-sense. The key contribution of the main result of this article is to develop the techniques to obtain error estimates between solutions of PDEs and approximating ANNs in the uniform $L^\infty $-sense. In particular, we prove that the number of parameters of an ANN to uniformly approximate the classical solution of the heat equation in a region $ [a,b]^d $ for a fixed time point $ T \in (0,\infty ) $ grows at most polynomially in the dimension $ d \in {\mathbb {N}} $ and the reciprocal of the approximation precision $ \varepsilon> 0 $. This verifies that ANNs can overcome the curse of dimensionality in the numerical approximation of the heat equation when the error is measured in the uniform $L^\infty $-norm.

Stability study of a model for the Klein-Gordon equation in Kerr space-time II

The present paper is a follow-up of our previous paper that derives a slightly simplified model equation for the Klein-Gordon equation, describing the propagation of a scalar field of mass $\mu$ in the background of a rotating black hole and, among others, supports the instability of the field down to $a/M \approx 0.97$. The latter result was derived numerically. This paper gives corresponding rigorous results, supporting instability of the field down to $a/M \approx 0.979796$.

Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows

This article studies a coupled system of model multi-dimensional partial differential equations (PDEs) that arise in the nonlinear dynamics of two-fluid Couette flow when insoluble surfactants are present on the interface. The equations have been derived previously, but a rigorous study of local and global existence of their solutions, or indeed solutions of analogous systems, has not been considered previously. The evolution PDEs are two-dimensional in space and contain novel pseudo-differential terms that emerge from asymptotic analysis and matching in the multi-scale problem at hand. The one-dimensional surfactant-free case was studied previously, where travelling wave solutions were constructed numerically and their stability investigated; in addition, the travelling wave solutions were justified mathematically. The present study is concerned with some rigorous results of the multi-dimensional surfactant system, including local well posedness and smoothing results when there is full coupling between surfactant dynamics and interfacial motion, and global existence results when such coupling is absent. As far as we know such results are new for non-local thin film equations in either one or two dimensions.

Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems.

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.

Calendar Anomalies or illusions? Evidence from Pakistan Stock Market

The stock market is the reflection of any country's economy around the globe, the purpose of the study was to figure out the anatomies of anomalies in the calendar, Year Turn Effect keeping the first month as Jan-Jul and last month as Jun-Dec, Month Turn Effect (First and Last Week of the month) and Week Turn Effect (First and Last day of the week) covering period for KSE-100 and KSE All shares from Jan-2001 to Jun-2019 and rest three indices were taken from inception date, EGARCH model was selected based on prescribed criterion AIC, SIC, and HQC test, and last results were retest with stock market sensitivity to key macroeconomic factors such as Interest Rate (KIBOR), Treasury Bills Rates, and Exchange Rate. Findings revealed a strong clustering feature impact on conditional variance on Year Turn, Month Turn, and Week Turn Effect with mixed of market returns. The research suggested four considerable factors (1) Events, (2) Role of Information, (3) Market Timing and (4) Sovereign Variable affection on market, further it also suggested for future research to stretch data set and employ the bootstrapping method and different statistical techniques for rigorous results.

Fermi's Golden Rule for Spontaneous Emission in Absorptive and Amplifying Media.

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.

Hydrodynamic Limit for an Active Exclusion Process

Collective dynamics can be observed among many animal species, and have given rise in the last decades to an active and interdisciplinary field of study. Such behaviors are often modeled by active matter, in which each individual is self-driven and tends to update its velocity depending on the one of its neighbors. In a classical model introduced by Vicsek and al., as well as in numerous related active matter models, a phase transition between chaotic behavior at high temperature and global order at low temperature can be observed. Even though ample evidence of these phase transitions has been obtained for collective dynamics, from a mathematical standpoint, such active systems are not fully understood yet. Significant progress has been achieved in the recent years under an assumption of mean-field interactions, however to this day, few rigorous results have been obtained for models involving purely local interactions. In this paper, as a first step towards the mathematical understanding of active microscopic dynamics, we describe a lattice active particle system, in which particles interact locally to align their velocities. We obtain rigorously, using the formalism developed for hydrodynamic limits of lattice gases, the scaling limit of this out-of-equilibrium system. This article builds on the multi-type exclusion model introduced by Quastel by detailing his proof and incorporating several generalizations, adding significant technical and phenomenological difficulties.

Communication-free autonomous cooperative circumnavigation of unpredictable dynamic objects

AbstractEach of several speed-limited planar robots is driven by the acceleration, limited in magnitude. There is an unpredictable dynamic complex object, for example, a group of moving targets or an extended moving and deforming body. The robots should reach and then repeatedly trace a certain object-dependent moving and deforming curve that encircles the object and also achieve an effective self-deployment over it. This may be, for example, the locus of points at a desired mean distance or distance from a group of targets or a single extended object, respectively. Every robot has access to the nearest point of the curve and its own velocity and “sees” the objects within a finite sensing range. The robots have no communication facilities, cannot differentiate the peers, and are to be driven by a common law. Necessary conditions for the solvability of the mission are established. Under their slight and partly unavoidable enhancement, a new decentralized control strategy is proposed and shown to solve the mission, while excluding inter-robot collisions, and for the case of a steady curve, to evenly distribute the robots over the curve and to ensure a prespecified speed of their motion over it. These are justified via rigorous global convergence results and confirmed via computer simulations.

Electrokinetic and in situ spectroscopic investigations of CO electrochemical reduction on copper

Rigorous electrokinetic results are key to understanding the reaction mechanisms in the electrochemical CO reduction reaction (CORR), however, most reported results are compromised by the CO mass transport limitation. In this work, we determined mass transport-free CORR kinetics by employing a gas-diffusion type electrode and identified dependence of catalyst surface speciation on the electrolyte pH using in-situ surface enhanced vibrational spectroscopies. Based on the measured Tafel slopes and reaction orders, we demonstrate that the formation rates of C2+ products are most likely limited by the dimerization of CO adsorbate. CH4 production is limited by the CO hydrogenation step via a proton coupled electron transfer and a chemical hydrogenation step of CO by adsorbed hydrogen atom in weakly (7 < pH < 11) and strongly (pH > 11) alkaline electrolytes, respectively. Further, CH4 and C2+ products are likely formed on distinct types of active sites.

Mixing rates for symplectic almost Anosov maps

We establish sharp bounds on the mixing rates of a class of two dimensional non-uniformly hyperbolic symplectic maps. This provides a primer on how to investigate such questions in a concrete example and, at the same time, it solves a controversy between previous rigorous results and numerical experiments.

Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials

We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. We employ the standard semi-implicit numerical scheme which treats the linear fourth-order dissipation term implicitly and the nonlinear term explicitly. Under natural constraints on the time step we prove strict phase separation and energy stability of the semi-implicit scheme. This appears to be the first rigorous result for the semi-implicit discretization of the Cahn-Hilliard equation with singular potentials.

Extremal statistics for stochastic resetting systems.

While averages and typical fluctuations often play a major role in understanding the behavior of a nonequilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the system is being done. In this context, the statistics of extreme fluctuations in contrast to the average plays an important role, as has been discussed in fields ranging from statistical and mathematical physics to climate, finance, and ecology. Herein, we study extreme value statistics (EVS) of stochastic resetting systems, which have recently gained significant interest due to its ubiquitous and enriching applications in physics, chemistry, queuing theory, search processes, and computer science. We present a detailed analysis for the finite and large time statistics of extremals (maximum and arg-maximum, i.e., the time when the maximum is reached) of the spatial displacement in such system. In particular, we derive an exact renewal formula that relates the joint distribution of maximum and arg-maximum of the reset process to the statistical measures of the underlying process. Benchmarking our results for the maximum of a reset trajectory that pertain to the Gumbel class for large sample size, we show that the arg-maximum density attains a uniform distribution independent of the underlying process at a large observation time. This emerges as a manifestation of the renewal property of the resetting mechanism. The results are augmented with a wide spectrum of Markov and non-Markov stochastic processes under resetting, namely, simple diffusion, diffusion with drift, Ornstein-Uhlenbeck process, and random acceleration process in one dimension. Rigorous results are presented for the first two setups, while the latter two are supported with heuristic and numerical analysis.

Persisting asymmetry in the probability distribution function for a random advection–diffusion equation in impermeable channels

In this paper, we study the effect of impermeable boundaries on the symmetry properties of a random passive scalar field advected by random flows. We focus on a broad class of nonlinear shear flows multiplied by a stationary, Ornstein–Uhlenbeck (OU) time varying process, including some of their limiting cases, such as Gaussian white noise or plug flows. For the former case with linear shear, recent studies (Camassa et al., 2019) numerically demonstrated that the decaying passive scalar’s long time limiting probability distribution function (PDF) could be negatively skewed in the presence of impermeable channel boundaries, in contrast to rigorous results in free space which established the limiting PDF is positively skewed (McLaughlin and Majda, 1996). Here, the role of boundaries in setting the long time limiting skewness of the PDF is established rigorously for the above class using the long time asymptotic expansion of the N-point correlator of the random field obtained from the ground state eigenvalue perturbation approach proposed in Bronski and McLaughlin (1997). Our analytical result verifies the conclusion for the linear shear flow obtained from numerical simulations in Camassa et al. (2019). Moreover, we demonstrate that the limiting distribution is negatively skewed for any shear flow at sufficiently low Péclet number. We demonstrate the convergence of the Ornstein–Uhlenbeck case to the white noise case in the limit γ→∞ of the OU damping parameter, which generalizes the results for free space in Resnick (1996) to the channel domain problem. We show that the long time limit of the first three moments depends explicitly on the value of γ, which is in contrast to the conclusion in Vanden Eijnden (2001) for the limiting PDF in free space. To find a benchmark for theoretical analysis, we derive the exact formula of the N-point correlator for a flow with no spatial dependence and Gaussian temporal fluctuation, generalizing the results of Bronski et al. (2007). The long time analysis of this formula is consistent with our theory for a general shear flow. All results are verified by Monte-Carlo simulations.

A competency framework for coaches working in coaching development centres

Orientation: Globalisation and the new world of work has changed the labour market, resulting in highly complex, volatile and dynamic environments. Organisations are dependent on highly skilled human capital to not only survive but also thrive. Selecting and developing talent is thus becoming a business necessity. Assessment centres (ACs) and development assessment centres (DACs) have become popular tools to manage talent because of the successful outcomes it provides. In recent years, there has been a noticeable increase in the awareness of the benefits that coaching can offer in the AC environment as well as the development of coaching development centres (CDCs). However, research on CDCs is still limited. For CDCs to provide the same rigorous results as ACs and ADCs, a well-defined competency framework is needed for coaches working in a CDC.Research purpose: The aim of this study was to explore the required competencies and formulate a competency framework for coaches working in a CDC.Motivation for the study: Coaching, which is at the heart of coaching practices such as executive coaching, one-on-one coaching, team coaching and CDCs, requires a clear set of coaching competencies to ensure that it deliver its mandate to its clients: individuals, organisations and the profession. Coaches in a CDC environment work in a different context and require different competencies. A competency framework for CDC specifically is therefore needed.Research approach/design and method: Adopting a qualitative methodology, a self-completed questionnaire was administered to eight participants, followed by a semi-structured interview. Lastly, the competency framework was verified by an expert panel of five experts using the Delphi technique.Main findings: A final competency framework consisting of 25 competencies, of which 14 are considered as core competencies, was validated.Practical/managerial implications: The study contributes to the understanding of the unique behavioural demands associated with coaches operating in the context of a CDC. It provides a conceptual and practical framework of what competencies are needed to work successfully and effectively as a coach in a CDC, and ultimately enhance the effectiveness of a CDC.Contribution/value-add: Utilising this framework in practice will enable us to use candidates best suited to the role of a coach at a CDC, and will enhance the overall success of such centres.