Discrete Case Research Articles

Preference Variation: Where Does Health Risk Attitude Come Into the Equation?

ObjectivesDecisions about health often involve risk, and different decision makers interpret and value risk information differently. Furthermore, an individual’s attitude toward health-specific risks can contribute to variation in health preferences and behavior. This study aimed to determine whether and how health-risk attitude and heterogeneity of health preferences are related. MethodsTo study the association between health-risk attitude and preference heterogeneity, we selected 3 discrete choice experiment case studies in the health domain that included risk attributes and accounted for preference heterogeneity. Health-risk attitude was measured using the 13-item Health-Risk Attitude Scale (HRAS-13). We analyzed 2 types of heterogeneity via panel latent class analyses, namely, how health-risk attitude relates to (1) stochastic class allocation and (2) systematic preference heterogeneity. ResultsOur study did not find evidence that health-risk attitude as measured by the HRAS-13 distinguishes people between classes. Nevertheless, we did find evidence that the HRAS-13 can distinguish people’s preferences for risk attributes within classes. This phenomenon was more pronounced in the patient samples than in the general population sample. Moreover, we found that numeracy and health literacy did distinguish people between classes. ConclusionsModeling health-risk attitude as an individual characteristic underlying preference heterogeneity has the potential to improve model fit and model interpretations. Nevertheless, the results of this study highlight the need for further research into the association between health-risk attitude and preference heterogeneity beyond class membership, a different measure of health-risk attitude, and the communication of risks.

Nonuniform input-output criteria for exponential expansiveness of discrete dynamical systems and applications

The aim of this paper is to present a new and complete study based on input-output methods for exponential expansiveness of discrete variational systems, treating both the nonuniform behavior and the uniform one. We continue the line of studies initiated in Dragičević et al. (2020) [19] and Dragičević et al. (2022) [20], providing a new approach in exploring the expansiveness properties. We associate to a discrete variational system a control type system that consists of a family of input-output discrete-time equations defined between two sequence spaces whose norms are translations invariant and we introduce new concepts of exact admissibility that rely on nonuniform local conditions. First, by imposing some minimal hypotheses on the input space or respectively on the output space, we establish connections between the exact admissibilities and the nonuniform exponential expansiveness. Moreover, we give for the first time a complete description of the structure of exactly admissible pairs that can be considered to explore nonuniform expansive behaviors in the discrete variational case. In addition, all the hypotheses on the classes from which we choose the input or the output spaces are motivated by illustrative examples. Next, we present characterizations for uniform exponential expansiveness via certain nonuniform exact admissibilities and we generalize the recent criteria for expansiveness of dynamical systems from Dragičević et al. (2020) [19]. Furthermore, we show via relevant examples that the results are the most general and the working hypotheses cannot be weakened or removed. As application, we give general criteria for uniform exponential expansiveness of skew-product semiflows in terms of nonuniform admissibility properties with sequence spaces invariant under translations.

Decreasing minimization on base-polyhedra: relation between discrete and continuous cases

This paper is concerned with the relationship between the discrete and the continuous decreasing minimization problem on base-polyhedra. The continuous version (under the name of lexicographically optimal base of a polymatroid) was solved by Fujishige in 1980, with subsequent elaborations described in his book (1991). The discrete counterpart of the dec-min problem (concerning M-convex sets) was settled only recently by the present authors, with a strongly polynomial algorithm to compute not only a single decreasing minimal element but also the matroidal structure of all decreasing minimal elements and the dual object called the canonical partition. The objective of this paper is to offer a complete picture on the relationship between the continuous and discrete dec-min problems on base-polyhedra by establishing novel technical results and integrating known results. In particular, we derive proximity results, asserting the geometric closeness of the decreasingly minimal elements in the continuous and discrete cases, by revealing the relation between the principal partition and the canonical partition. We also describe decomposition-type algorithms for the discrete case following the approach of Fujishige and Groenevelt.

Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity

In this paper, we are interested in solving a Cauchy inverse problem in linear elasticity. For this, we propose a new method based on Robin conditions on the inaccessible boundary, then we study the convergence and regularizing property of the proposed algorithm. We use the finite element method for the discretization of our problem. Further, we treat the spectrum analysis of the discrete problem in order to study the convergence behavior of the proposed method in the discrete case. Finally, we present numerical results which show the efficiency and stability of the proposed approach in the presence of perturbed data. The robustness of the proposed algorithm is also performed for the anisotropic and heterogeneous cases.

A Mean-Field Approximation of SIR Epidemics on an Erdös-Rényi Network Model.

The stochastic nature of epidemic dynamics on a network makes their direct study very challenging. One avenue to reduce the complexity is a mean-field approximation (or mean-field equation) of the dynamics; however, the classic mean-field equation has been shown to perform sub-optimally in many applications. Here, we adapt a recently developed mean-field equation for SIR epidemics on a network in continuous time to the discrete time case. With this new discrete mean-field approximation, this proof-of-concept study shows that, given the density of the network, there is a strong correspondence between the epidemics on an Erdös-Rényi network and a system of discrete equations. Through this connection, we developed a parameter fitting procedure that allowed us to use synthetic daily SIR data to approximate the underlying SIR epidemic parameters on the network. This procedure has improved accuracy in the estimation of the network epidemic parameters as the network density increases, and is extremely cheap computationally.

Forecasting Model of Air Pollution Index using Generalized Autoregressive Conditional Heteroskedasticity Family (GARCH)

The Air Pollution Index (API) of Malaysia has increased consistently in recent decades, becoming a serious environment issue concern. In this paper, we analyzed daily integer value time series data for API in Sarawak from January to June in 2019 using generalized autoregressive conditional heteroskedasticity (GARCH) family for discrete case namely poisson integer value GARCH (INGARCH), negative binomial integer value GARCH (NBINGARCH) and integer value autoregressive conditional heteroskedasticity (INARCH) models. The parameters of the models will be estimated using quasi likelihood estimator (QLE) and we compare their Akaike information criterion (AIC) to determine the best model fitted the data. The results showed that INGARCH (1,1) and INARCH (1,0) performed inconsistent results since the conventional methods of NBINGARCH (1,1) outperformed the performance of INGARCH (1,1) and INARCH (1,0). However, consistet results were achieved as the NBINGARCH (1,1) gave the smallest forecasting error compared to INGARCH (1,1) and INARCH (1,0). The findings are very important for controlling the API results in future and taking protection measure for conservation of the air.

Heliodorus’ <i>Aethiopica</i>: A New Patristic Context

This article argues that reading Heliodorus’ Aethiopica alongside post-Nicene Patristic texts sheds new light on its place within the multifaceted religious world of Late Antiquity. Through an analysis of three discrete test cases, this article brings to light the complexities of the Aethiopica’s incorporation of ideas which are prominent in contemporary Christian thought. In so doing, it presents new evidence for the fourth-century context in which Heliodorus produced his work.

Decolonizing International Law?

Abstract This article analyzes the way that political actors, advocate lawyers, and European administrators leveraged the designations political prisoner, political refugee, and prohibited immigrant to claim rights for inhabitants of the UN trust territories of French Cameroon and British Cameroons in the 1950s. Incarcerated activists identified themselves as political prisoners as they claimed that their human rights were upheld by international legal norms outlined in UN documents such as the Charter, the Universal Declaration of Human Rights, and the Trusteeship Agreements, which bound administering authorities to uphold these principles. Having imposed politics onto the prison, Cameroonian nationalists who escaped repression in French Cameroon by fleeing to British territory politicized their exile as they claimed refugee status in British Cameroons, a territory they viewed as belonging to the nation they envisioned. In so doing, Cameroonian nationalists revealed embryonic refugee law to be more aspirational than universally applicable—but nonetheless laid claim to its protections in ways that did, in some cases, sway the courts. The focus on the legal cases of political prisoners and refugees shows how Cameroonian nationalists viewed the rights that international law established or promised as legitimizing their anti-colonial revolutionary state-building project. With the advocate lawyers who represented them, legally minded Cameroonian nationalists acted, defended, and claimed as though the trusteeship system had universalized a decolonized international law. Contributing to emerging scholarship on the relation of international law to global inequality in the decolonizing age, this article gives an account of a decolonizing worldmaking at the grassroots, where, through discrete legal cases, actors practiced articulating anti-colonial revolution with international law, contesting it and shaping it to their aspirations.

Banknotes of the Irish Free State

This article considers the banknotes printed in the Irish Free State as discrete case studies in order to examine the aesthetic debates of the 1920s, between the rural and the urban; insularism and internationalism; between the decision to foster native artists or present an outward-looking nation by commissioning the most renowned artists outside of Ireland; between choosing the visual representation of partition or its symbolic erasure. The focus of the article is the first series of legal tender notes known as the ‘Lady Lavery Series’, issued from 10 September 1928, and the consolidated banknotes, referred to as the ‘Ploughman Series’, first issued between May and June 1929. The collaboration of artists, including John Lavery, Dermod O’Brien and E. L. Lawrenson, and government institutions, namely the Currency Commission and the Department of Finance, are considered, with specific attention to the design and reception of the two series of banknotes. The intermediary role of the banknotes advisory committee – consisting of art experts Thomas Bodkin, Dermod O’Brien and Lucius O’Callaghan – illuminate both the practical and aesthetic considerations weighed up by the artists and state institutions. The under-examined design processes behind the Free State banknotes are placed within the wider context of state-run commissions and competitions – coinage, postage stamps, official seals – that helped shape a distinctive visual identity for Ireland in the 1920s.

Continuous and discrete zeroing neural network for a class of multilayer dynamic system

Multilayer dynamic system is widely used in industry and other fields. Different from common systems, multilayer dynamic system has complex structure leading to challenges for research. In this paper, we study zeroing neural network(ZNN) models for a class of multilayer dynamic system(MLDS). In the case of continuous time, continuous ZNN models for continuous MLDS (MLDS-linear-ZNN, MLDS-nonlinear-ZNN and MLDS-noise-tolerant-ZNN) are proposed based on ZNN design method with theoretical analysis. In the discrete case concurrently, discrete ZNN models (MLDS-linear-mDZNN, MLDS-nonlinear-mDZNN and MLDS-noise-tolerant-mDZNN) with m-step ZeaD formula, a new Zhang et al. discretization formula presented in previous paper, are put forward and corresponding discrete algorithms are obtained. Finally, numerical experiments are carried out to verify the superiority and maneuverability of ZNN models for MLDS proposed in this paper.

A hybrid discrete–continuum framework for modelling filtration

Typical mathematical frameworks for modelling the blocking behaviour of a filter due to particle deposition fall into one of two categories: a continuum approximation, whereby particle deposition is assumed to occur in such a way that all pores in the material are in the same state of blocking at any given time; or a discrete model, where blocking is treated as individual events in both space and time. While the former is computationally inexpensive, the latter allows for variation from pore to pore. This pore-to-pore variation has been shown to provide a qualitative change in the observed filtration behaviour that is essential to reproduce experimental observations. We present a hybrid model that describes the location of particle depositions in a continuum manner while retaining a discrete, stochastic component to capture the time at which a blocking event occurs. The model is able to grade between the aforementioned extreme continuum and discrete cases through a parameter that controls the spatial extent of a blocking event. This enables us to uncover the way in which the nature of the blocking process changes between these two pre-existing models. The model also captures the key ingredients of a fully discrete stochastic model at a fraction of the computational cost, making it ready to use to describe other complex filtration scenarios.

Stabilization of a System of Unstable Pendulums: Discrete and Continuous Case

Stabilization of a System of Unstable Pendulums: Discrete and Continuous Case

A Contribution to the Filter Design for a Class of Linear Singular Delayed Systems: The Discrete Time Case

A Contribution to the Filter Design for a Class of Linear Singular Delayed Systems: The Discrete Time Case

Mixture discrete reversed hazard rate and its main properties

The reversed hazard rate, defined as the ratio of the density to the distribution function, has recently drawn great interest in reliability and survival analysis due to its usefulness in the analysis of left-censored data. This paper develops the mixture model of discrete reversed hazard rates and studies its main properties. Similar to the continuous case, results of the bending property for the reversed hazard rate in discrete case are studied. In addition, mixtures of the mean inactivity time, which are closely related to the reversed hazard rate, are discussed and the corresponding results of its bending property are also investigated. Preservation of aging properties under both mixtures of reversed hazard rate and mean inactivity time is discussed as well. As a special case, the proportional discrete reversed hazard rate model is presented and the bending properties for this case are also discussed. Finally, stochastic comparisons of the mixture discrete reversed hazard rates of two mixed populations are addressed.

Continuous-Variable Nonlocality and Contextuality

Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the other hand, continuous-variable scenarios offer some of the most promising candidates for implementing quantum computations and informatic protocols. Here we set out a framework for treating contextuality in continuous-variable scenarios. It is shown that the Fine–Abramsky–Brandenburger theorem extends to this setting, an important consequence of which is that Bell nonlocality can be viewed as a special case of contextuality, as in the discrete case. The contextual fraction, a quantifiable measure of contextuality that bears a precise relationship to Bell inequality violations and quantum advantages, is also defined in this setting. It is shown to be a non-increasing monotone with respect to classical operations that include binning to discretise data. Finally, we consider how the contextual fraction can be formulated as an infinite linear program. Through Lasserre relaxations, we are able to express this infinite linear program as a hierarchy of semi-definite programs that allow to calculate the contextual fraction with increasing accuracy.

Output feedback [formula omitted] control of positive Markov jump systems: A dynamic event-triggered method

The output feedback l1 control problems of positive Markov jump systems(PMJSs) are studied using event-triggered method in this paper. Firstly, two novel dynamic output event-triggered control strategies(DOETCS) are proposed for continuous-time PMJSs as well as discrete-time PMJSs, which can reduce the event-triggered frequency and save network resources. Then, by constructing multiple linear copositive Lyapunov functions, two sufficient conditions about positivity and stochastic stability with l1-gain performance are presented for the continuous-time closed-loop PMJSs and the discrete-time closed-loop PMJSs. Simultaneously, two desired output feedback l1 controllers and two DOETCS are also co-designed to stabilize the PMJSs in continuous and discrete cases, respectively. All the conditions obtained in this paper are in the form of linear programming(LP). Further more, the influence of parameters in the novel DOETCS on the event-triggered frequency is investigated in detail in the section of numerical simulation. Finally, two numerical examples are provided to verify the effectiveness of the proposed design schemes.

Tear Trough Filler Techniques Utilizing Hyaluronic Acid: A Systematic Review.

Hyaluronic acid soft-tissue augmentation fillers are commonly injected into multiple areas of the face, including the tear trough. Despite well-documented risks, there is no standardized, evidence-based approach to inject filler in this area, be it using a hypodermic needle or a microcannula. The authors, therefore, sought to establish a preference between the two methods to facilitate progression toward standardization and prevention of adverse events. This is a systematic review of articles discussing hyaluronic acid tear trough injection techniques performed in vivo and related outcomes. Searches were conducted across The Cochrane Library, PubMed, Scopus, Web of Science, and Embase to yield relevant articles published before February of 2020. All selected articles incorporated discrete patient cases and were analyzed by a variety of variables assessing evidence strength, outcomes, technique, and patient safety. After appraisal, 42 articles met eligibility criteria: 20 using needles, 12 using cannulas, and 10 focusing on adverse events. Level III was the most commonly awarded evidence grade, corresponding to retrospective, nonexperimental descriptive studies. There were no statistically significant differences in reported aesthetic results, patient satisfaction, or incidence of adverse events across the needle-based and cannula-based articles. Some technique trends, such as targeted anatomical plane and needle position, emerged in subsequent articles. Given that there were no statistically significant differences in patient safety or outcomes, an evidence-based preference for needle or cannula injection into the tear trough cannot be made at this time. Current inconsistencies make tear trough injection procedures difficult to replicate, making standardization based on avoidance of adverse events not feasible.

On Reconstructing Parts of Quantum Theory from Two Related Maximal Conceptual Variables

In the book Helland (2021) the general problem of reconstructing the Hilbert space formulation in quantum theory is discussed from the point of view of what I called conceptual variables, any variables defined by a person or by a group of persons. These variables may be inaccessible, i.e., impossible to assign numerical value to by experiments or by measurements, or accessible. One basic assumption in Helland (2021) and here is that group actions g ∈ G are defined on a space where some maximally accessible variable varies, and then accessible functions of these maximal variables are introduced. By using group representation theory the basic Hilbert space formalism is restored under the assumption that the observator or the set of observators has two related maximally accessible variables in his (their) mind(s). The notion of relationship is precisely defined here. Symmetric (self-adjoint) operators are connected to each variable, and in the discrete case the possible values of the variables are given by the eigenvalues of the operators. In this paper the main results from Helland (2021) are made more precise and more general. It turns out that the conditions of the main theorem there can be weakened in two essential ways: 1) No measurements need to be assumed, so the result is also applicable to general decision situations; 2) States can have arbitrary phase factors. Some consequences of this approach towards quantum theory are also discussed here.

Nailed it! Doctor of pharmacy learners' self-awareness of performance on authentic assessments

IntroductionThe primary objective of this pilot study was to determine the reliability and validity of an objective structured clinical examination (OSCE) self-awareness survey. A secondary objective was to assess learner self-awareness in OSCE performance. MethodsA retrospective review of OSCE data from a single cohort in a three-year accelerated doctor of pharmacy program occurred. The cohort completed four OSCEs with a total of 23 discrete cases. At the end of each case, before receiving feedback, learners completed an evaluation of their skills, communication, overall performance, and identified if they believed the patient/provider would return (“nailed or failed”). These self-evaluations were then compared with respective learner performance scores for each case. Content validity was assessed for the self-awareness survey via the Lawshe method. Reliability of the OSCE cases and self-awareness survey were conducted utilizing Cronbach's alpha and the Spearman-Brown formula, respectively. ResultsThe OSCE self-awareness survey was found to be face valid and reliable for the overall survey. The subsections of return to pharmacist and overall learner performance were also found to be valid and reliable. A statistical relationship was found between learner self-assessment of pass/fail and their actual grade for overall performance and return to pharmacist. ConclusionsResults from this study may guide remediation plans related to OSCE performance and development of other self-awareness activities in practice settings. Further studies are needed to evaluate the broader application and use of self-awareness tools.

Frames of solutions and discrete analysis of pseudo‐differential equations

We construct discrete analogs of multidimensional singular integral operators and study their invertibility. Moreover, we give a comparison between continual and discrete case. We give the theory of periodic Riemann problem also, because it is needed for studying invertibility of so‐called paired equations. For more general case of pseudo‐differential operators, we construct the solvability theory for discrete pseudo‐differential equations in discrete analogs of Sobolev–Slobodetskii spaces. Some comparison results for discrete and continuous solutions are given also in appropriate discrete normed spaces.