Imaginary Case Research Articles

Third homology of SL2 over number fields: The norm-Euclidean quadratic imaginary case

In the article The third homology ofSL2(Q) ([7]), Hutchinson determined the structure of H3(SL2(Q),Z[12]) by expressing it in terms of K3ind(Q)≅Z/24 and the scissor congruence group of the residue field Fp with p a prime number. In this paper, we develop further the properties of the refined scissors congruence group in order to extend this result to the case of imaginary quadratic number fields whose ring of integers is a Euclidean domain with respect to the norm.

Diophantine approximation with prime denominator in real quadratic function fields

In the thirties of the last century, I.M. Vinogradov proved that the inequality ||pα||≤p−1/5+ε has infinitely prime solutions p, where ||.|| denotes the distance to a nearest integer. This result has subsequently been improved by many authors. In particular, Vaughan (1978) replaced the exponent 1/5 by 1/4 using his celebrated identity for the von Mangoldt function and a refinement of Fourier analytic arguments. The current record is due to Matomäki (2009) who showed the infinitude of prime solutions of the inequality ||pα||≤p−1/3+ε. This exponent 1/3 is considered the limit of the current technology. Recently, in [3], the authors established an analogue of Matomäki's result on imaginary quadratic extensions of the function field k=Fq(T). In this paper, we consider the case of real quadratic extensions of k of class number 1, for which we prove a function field analogue of Vaughan's above-mentioned result (exponent θ=1/4). Our method uses versions of Vaughan's identity and the Dirichlet approximation theorem for function fields. The latter was established by Arijit Ganguly in the appendix to our previous paper [3] on the imaginary quadratic case. We also simplify arguments in the paper [1] on the same problem for real quadratic number fields by D. Mazumder and the first-named author.

Worldview literacy as a part of teacher professionalism

ABSTRACT This article, based on a mixed-method study, examines which dimensions of worldview are addressed by a group (N = 134) of Finnish students and in-service educators when interpreting a written imaginary case from everyday school life. The findings are interpreted in the framework of worldview literacy, derived from the concept of religious literacy and defined as an ability to decipher situations with aspects of worldview diversity. Data from open responses to a survey were approached in two ways, quantitatively, where worldview literacy was seen as an ability to recognise the impact of worldview in the case and argue for it, and qualitatively, where the different aspects of worldview mentioned by the participants were analysed. In terms of the quantitative analysis, the survey revealed a tendency to avoid explaining situations through worldview. From a qualitative point of view, the participants most often mentioned worldview as beliefs and something deeply significant and emotional. Furthermore, the data raised questions about essentialist attitudes towards worldviews and cultures, and recognising power issues. The case-based open question yielded multifaceted data, pointing to the fact that this method could be developed to measure worldview literacy.

Quadratic fields admitting elliptic curves with rational j-invariant and good reduction everywhere

Clemm and Trebat-Leder (2014) proved that the number of quadratic number fields with absolute discriminant bounded by x over which there exist elliptic curves with good reduction everywhere and rational j-invariant is ≫xlog−12⁡(x). In this paper, we assume the abc-conjecture to show the sharp asymptotic ∼cxlog−12⁡(x) for this number, obtaining formulae for c in both the real and imaginary cases. Our method has three ingredients:(1)We make progress towards a conjecture of Granville: Given a fixed elliptic curve E/Q with short Weierstrass equation y2=f(x) for reducible f∈Z[x], we show that the number of integers d, |d|≤D, for which the quadratic twist dy2=f(x) has an integral non-2-torsion point is at most D23+o(1), assuming the abc-conjecture.(2)We apply the Selberg–Delange method to obtain a Tauberian theorem which allows us to count integers satisfying certain congruences while also being divisible only by certain primes.(3)We show that for a polynomially sparse subset of the natural numbers, the number of pairs of elements with least common multiple at most x is O(x1−ϵ) for some ϵ>0. We also exhibit a matching lower bound. If instead of the abc-conjecture we assume a particular tail bound, we can prove all the aforementioned results and that the coefficient c above is greater in the real quadratic case than in the imaginary quadratic case, in agreement with an experimentally observed bias.

On Farrell–Tate cohomology of GL3 over rings of quadratic integers

The goal of the present paper is to push forward the frontiers of computations on mod ℓ Farrell–Tate cohomology for arithmetic groups. We deal with ℓ-rank 1 cases different from PSL2. The conjugacy classification of cyclic subgroups of order ℓ is reduced to the classification of modules of Cℓ-group rings over suitable rings of integers which are principal ideal domains, generalizing an old result of Reiner. As an example of the number-theoretic input required for the Farrell–Tate cohomology computations, we discuss in detail the homological torsion in PGL3 over principal ideal rings of quadratic integers, accompanied by machine computations in the imaginary quadratic case.

Missing aspects of the risk: speed and duration

Purpose- Risk assessment, risk prioritization and risk responding are vital steps in any risk management process. After risks are identified, traditional approach allows risk experts to define likelihood and impact factors for these risks. Thus, a risk severity can be defined, and risk prioritization can be considered under the budget constraints, i.e., cost of implementing remedial measures. On the other hand, recent events, like digitalization and pandemic, showed that evaluating only these two factors of the risk can be missing. Two important aspects of the risk are suggested to be considered: speed (velocity) and duration. In this study, these two elements are analyzed. Methodology- In the study, following an introduction, COSO models and results of the literature review are analyzed. After a theoretical background and a literature review, a discussion on new aspects of the risk is started. Finally, an imaginary case is used to analyze risks including all aspects. Findings- It is realized that in the academic literature, new aspects of the risk have not been addressed yet. This is the reason why these two aspects defined as missing. At the end, it is concluded that although speed and duration are elements, which directly affect the impact factors, at the same time, these are key determinants of the timing and structure of the risk responses. Additionally, continuous risk assessment can be beneficial for the entities to have more time to respond to the risks. Conclusion- Depending on the findings, it is concluded that all aspects of the risk is needed to be analyzed during risk management processes. The originality of this study stems from the fact that it includes practical suggestions for integrating the concepts of speed and velocity, which are conceptually included into the frameworks. In addition, this study presents a perspective by associating the concepts of agility, resilience, and continuous risk assessment. Keywords: Risk assessment, COSO, risk management, internal control, internal audit. JEL Codes: G32, M42, M19

The Lockean Proviso and Orbital Sustainability—An Anthropological View

Over the last decades, we have witnessed the gradual commercialization of the Earth orbit. The exponential development of private space activities makes this distant natural field, with the overcoming of technological difficulties, more and more hospitable to free initiative and entrepreneurship. However, the orbital space is considered global commons. Through the imaginary case method, we intend to ponder on possible ways to legally regulate the exploitation of the orbital space, namely the application of Pigouvian taxes, on the sustainability of the orbital environment, through ethical considerations originating from the application of the Lockean proviso. Although they are designed to cover the damage caused by that particular polluting activity, which is difficult to estimate and, in our case, almost impossible to quantify in the long run, the Pigouvian taxes are the result of a proactive logic. The tension between civilization and nature turns the world outside the Earth into a wilderness destined for humanization, another area of exercise of the liberal self. Non-legal reasons for the sustainability of the orbital environment may arise from observing the Lockean principle of fair ownership. Between the prohibition of an unreasonable destruction of nature’s goods and the equitable access to extra-terrestrial resources, the human desire for appropriation updates the proviso destined for the colonization of America in the twenty-first century. Given that there are currently no plans to clean the technological waste in orbit, adopting the conservation of the orbital environment as an ethical principle could help to formulate a more environmentally responsible liberalism, as part of a long-term agenda of exploitation in the vicinity of our planet.

Simulated Wound Care as a Competence Assessment Method for Student and Registered Nurses.

To describe the development and use of a wound care simulation assessing RNs' and graduating student nurses' practical wound care competence and to describe observations of participants' wound care competence. A descriptive, qualitative design was used. Data were collected in 2019 from 50 healthcare professionals and students using a simulated wound care situation and an imaginary patient case. The simulation was based on a previously developed and tested wound care competence assessment instrument, which included a 14-item checklist that assesses practical wound care competence of chronic wounds. The data were analyzed and described based on the 14 competence areas or as other competencies. Participants showed competence in identification of wound infection, debridement, dressing selection, tissue type identification, and consultation. Participants' shortcomings were related to pain assessment and management, asepsis, offloading, and documentation. Simulation was shown to be a promising tool to assess healthcare professionals' and students' practical wound care competence in a safe and standardized situation. This study provided new information about simulation as a method to assess student nurses' and RNs' wound care competence. The results could be used in wound care education planning and development in both undergraduate nursing education and continuing education for nursing professionals.

Voting and MCDM: the pedagogy of the Saari triangle

Abstract The essay has a twofold objective: primarily, to present an application of voting theory as a possible evaluation method, and concurrently, to offer a pedagogic framework, based on that very application. Evaluation and certain notions of preference and value have common semantic roots. By equating preference and choice, we end up amidst social choice (SC) theory and voting methods, also manageable as joint decisions in multiple-criteria decision making (MCDM). With the aid of the Saari triangle some essential differences of pairwise and positional voting rules for up to three alternatives can be depicted. A voting or decision rule does not necessarily follow the true preferences of the actors, but may mirror the problematics of the chosen rule. The Saari triangle makes it possible to visualize some paradoxical results in the exemplary evaluations of digital websites through an imaginary case description via voting and MCDM. As candidates and voters in SC are put to stand for alternatives and criteria in MCDM, the methodological and pedagogical goals of the study are achieved.

No longer an imaginary case: Community, plans, and actions in canoeing rapids

ABSTRACT Background: We investigate the nature of planning the canoeing of rapids and its reasoning processes, while at the same time advancing a syncretic approach to cognitive and situative theories of learning. Building upon the work of Lucy Suchman, we examine how canoers plan to run rapids and how plans serve as resources for action. Methods: In ethnographically-informed manner, we followed a team of canoers across various contexts of rapid scouting and running. By mounting video cameras on canoeing dyads’ helmets, we captured the team’s discursive construction of plans, how canoe partners took up the collective production of plans to elaborate their own plans, and how plans seemed to function as resources for canoeing action. Findings: Through the analysis of three episodes of rapid running, we articulate detailed descriptions of reasoning processes at the collective, canoeing dyad and individual levels, and draw relationships between them to explain observed canoeing performance in its full complexity. Contribution: We show that drawing on intersections, affinities, and complementarities between principles and theoretical constructs from both cognitive and situative theories of learning may achieve a more holistic, multi-level, and fine-grained description of knowing and learning as ongoing, at once collective and individual achievements.

Newcomb dilemma in development management

Newcomb dilemmas show a discrepancy in our rational reasoning, as made clear by comparing Evidential Decision Theory with Causal Decision Theory. In this paper, I look at three versions of the dilemma: the original, highly technical and abstract one plus two more mundane cases. I also account for the general schema of the dilemma possibly appearing in macroeconomic situations. Ahmed (2014) aims to provide a solution for macroeconomic cases that opens room for forming a development management Newcomb dilemma – an imaginary case of electric motor competition between Toyota and Tesla. I argue that Ahmed’s solution may solve the macroeconomic Newcomb dilemma, but it cannot be applied to the development management dilemma. If I am right, similar Newcomb situations could be cropping up regularly in development management, leading to seemingly insoluble strategic decisions having to be made. This may create an inevitable pitfall for development management.

Comments on Deuring's zero-spacing phenomenon

We codify some aspects of Deuring's zero-spacing phenomenon, namely that in the presence of an exceptional Landau/Siegel zero, various product L-functions have their low-height zeros lie in a very regular pattern, nearly an arithmetic progression on the central line. This piece of “analytic number theory folklore” seems to have had its actual proof escape the literature in generality, yet we still claim to provide a “different” proof in that we use Lavrik's general method for approximate functional equations, rather than (say, in the imaginary quadratic case) a decomposition into Epstein ζ-functions and analysis with K-Bessel functions and Kloosterman sums.

Images of competition and their impact on modern macroeconomics*

Modern mainstream macroeconomics is characterised by its reliance on a general equilibrium framework of Walrasian origins, which is crucially associated with perfect competition and statics. To cope with the real economy, macroeconomics has been “forced” to introduce imperfections and frictions of various kinds into the perfectly competitive model. This raises, argues the paper, significant conceptual and analytical difficulties and tensions. There exist, however, other views of competition and markets which could provide more solid and fruitful foundations to the analysis of the macro-economy. After a selective examination of some contributions to the development of the notion of perfect competition, the paper looks at how modern mainstream macroeconomics dealt with general equilibrium and deviations from it. The paper argues that these alleged deviations from the perfectly competitive case should rather be regarded as inherent features of market economies. Dealing with them more satisfactorily requires calling on a different view of the working of the economy instead of trying to correct and amend the imaginary case of perfect competition.

Nonsense on Stilts - Part 1: The ICER 2020-2023 Value Assessment Framework for Constructing Imaginary Worlds.

Previous commentaries in the Formulary Evaluation section of INNOVATIONS in Pharmacy have pointed to the lack of credibility in modeled claims for cost-effectiveness and associated recommendations for pricing and access by the Institute for Clinical and Economic Review (ICER). The principal objection to ICER reports has been that their modeled claims fail the standards of normal science: they are best seen as pseudoscience. The purpose of this latest commentary is to provide a critique of the recently released ICER 2020 Value Assessment Framework (VAF). Although ICER has taken upon itself the pole position in health technology assessments and recommendations for product pricing in the US health care system, the incremental, lifetime cost-per-QALY modeling methodology should not be taken seriously. The creation of imaginary modeled worlds, built entirely from assumption, fails the demarcation test between science and pseudoscience. The ICER evidence reports are best seen as the health technology assessment equivalent of 'intelligent design' in counterpoint to 'natural selection'. It is surprising, therefore, that health care decision makers should take ICER's recommendations seriously as providing 'approximate information' for formulary decision making. What is not appreciated is that the claims made by ICER lack credibility, are impossible to evaluate and lack the ability to be replicated across treatment settings. Indeed, the models presented under the guise of a 'state of the art' value assessment were never intended to support evaluable claims. We have no idea and will never know if they are right or if they are wrong. ICER's position becomes even more untenable once the models presented are assessed in detail. Without in any way supporting the ICER methodology, it is worth noting that all too often ICER's claims for incremental QALYs in specific models are based upon what appears to be, from the limited evidence presented, a casual and ad hoc assemblage of utility scores from diverse constructs. This is a critical weakness given the role attributed by ICER to the modeled cost-per-QALY claims as central to ICERs imaginary value assessment. ICER also overlooks the fact that the utility scores it captures from the literature to populate its imaginary reference case world lack objectivity. They are ordinal rather than interval measures. To apply these manifest scores to time spent in a disease stage and then aggregate these over different disease stages is nonsensical. The critical issue is one of instrument development. The case made here is for the application of Rasch Measurement Theory (RMT) to construct a unidimensional instrument with interval properties, in this case from the needs fulfillment construct of quality of life (QoL). Unless an instrument meets RMT standards in its development, the logic of Rasch modeling to achieve fundamental measurement standards means that other scales are, by definition, ordinal. It is absurd to 'assume' they are interval. RMT is designed to create instruments to evaluate change and test hypotheses. In the absence of instruments that have RMT properties, the cost-per-QALY reference case modelling meme collapses. It is an analytical dead end. If we are to support a meaningful scientific program to discover new facts to support health care delivery and improve the lives of patients, caregivers and their families, then ICER should be put to one side.

H-Index and Its Variants

H-index is an accepted norm to rank scientists and makes them eligible for various professional benefits. However, taking into consideration the associated flaws of the h-index, a diversified set of parameters have been proposed by the scientific community to rank authors in a better way. Imaginary case studies and datasets are used to find out the practical and actual utility of the proposed indicators. To analyze the individual behaviour of each index, these indices are comprehensively evaluated on an extensive data set. This study emphasizes the scrutiny of the h-index, some of its variants, and extensions to rank authors. There appears to be a correlation between high citation rates for a published researcher and the award of prestigious accolades. Thus, the inclusion of a researcher in the list is based on high citation rates and the authority has claimed a direct connection between the citation rates and prestigious awards. In this context, the work initiated to find out the h-index and its variants for the selected researchers incorporated in the hall of citation laureates from the field of medicine. It is clear from the correlation analysis that there is a difference in the degree of correlation between the h-index and its variants. The A-index is weakly correlated, and M-Quotient is strongly correlated with h-index. Thus, most of the h-index variants are merely mathematically and arithmetically modified and does not add any new information as these are highly correlated and are based on the h-core. Thus, more useful and reasonable approaches could be developed for multidimensional and contextualized evaluations of scientific performance rather than cocooning them with mere numbers.

HEURISTICS FOR -CLASS TOWERS OF REAL QUADRATIC FIELDS

AbstractLet $p$ be an odd prime. For a number field $K$, we let $K_{\infty }$ be the maximal unramified pro-$p$ extension of $K$; we call the group $\text{Gal}(K_{\infty }/K)$ the $p$-class tower group of $K$. In a previous work, as a non-abelian generalization of the work of Cohen and Lenstra on ideal class groups, we studied how likely it is that a given finite $p$-group occurs as the $p$-class tower group of an imaginary quadratic field. Here we do the same for an arbitrary real quadratic field $K$ as base. As before, the action of $\text{Gal}(K/\mathbb{Q})$ on the $p$-class tower group of $K$ plays a crucial role; however, the presence of units of infinite order in the ground field significantly complicates the possibilities for the groups that can occur. We also sharpen our results in the imaginary quadratic field case by removing a certain hypothesis, using ideas of Boston and Wood. In the appendix, we show how the probabilities introduced for finite $p$-groups can be extended in a consistent way to the infinite pro-$p$ groups which can arise in both the real and imaginary quadratic settings.

ICER, ISPOR AND QALYs: Tales of Imaginary Worlds.

Previous commentaries in the Formulary Evaluation section of INNOVATIONS in Pharmacy have pointed to the lack of credibility in modeled claims for cost-effectiveness and associated recommendations for pricing by the Institute for Clinical and Economic Review (ICER). The principal objection to ICER reports has been that their modeled claims fail the standards of normal science: they are best seen as pseudoscience. The purpose of this latest commentary is twofold: first, to review the latest report by the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) on standards and value claims for modeling imaginary cost-per-quality life year(QALY) worlds in health technology assessments and (ii) given ICER's commitment to ISPOR standards, to consider thecredibility of ICER's QALYs. The concern is that ICER gives the impression that there is a common and agreed utility metric to support QALY constructs and that there is an agreed standard for creating QALYs within the imaginary reference case meme. The purpose of this commentary is to emphasize that there is no 'gold standard' QALY, let alone a 'gold standard' utility metric. A QALY is what you assume the QALY should be; it is an artificial construct which allows any number of competing QALYs to be generated for the same target population under different imaginary constructs. Similar objections apply to the application of willingness-to-pay thresholds to support ICER's business case as the sole arbiter, in pole position, of health technology assessments to support pricing recommendations. In the US. A threshold has to be defined for the QALYs and costs captured, by assumption, within the model. Even for the same target patient population a $50,000 cost per QALY threshold will yield different pricing recommendations depending upon the assumptions driving the QALY estimate, such as choice of utility metric, time spent by stage of disease, frequency and severity of adverse events and costs. While this is an obvious point, it appears not to occur to those who, with a limited technical understanding of how the ICER model is constructed (and ICER is not given to extended technical explanations) take at face value the ICER imaginary construct and the QALY value judgements. Of course, it is also beside the point that the ICER reference case imaginary world was never intended to support empirical assessments of the claims made; we have no idea of whether it is right, if it is wrong and, over the lifetime perspective, we will never know and were never intended to know.

Giving Useful but Not Well-Understood Ideas Their Due

AbstractIn this paper, I introduce the ideas to be discussed in the articles of this journal with reference to an imaginary case involving a pregnant woman declared dead on the basis of neurological criteria. I highlight the fact that although these ideas have proved useful for advancing certain claims in bioethical debates, their implications are not always well understood and may complicate our arguments. The ideas to be discussed are (1) an ethic internal to the profession of medicine; (2) the difference between killing and letting die; (3) the organism as a whole; and (4) the “lives” and interests of the dead.

The Imaginary Worlds of Cure Proportion Modeling: Survivorship and Reference Case Pricing of Transformative Therapies.

On August 6, 2019 the Institute for Clinical and Economic Review (ICER) released a set of proposed adaptations to its value assessment framework methods where the intervention under review was considered a 'single or short-term transformativetherapy' (SST). These adaptations are intended to 'complement and build upon the upcoming update to the overall ICER assessment framework…'. The purpose of this commentary is to review the proposed cure proportion modeling reference case framework for assessing the value of SSTs together with ICER's 'recommendations for fair value-based pricing …'. Following previous commentaries on the ICER value assessment framework, the question raised is whether the proposed cure proportion modeling standards meet those of normal science: is the modeling proposed capable of generating value claims for the intervention that are credible, evaluable and replicable? The proposed standards for transformative therapies do not change the underlying commitment to reference case modeling. At the same time, the cure proportion modeling proposed adaptations have to be seen in the context of the concerns expressed by ICER that their reference case model can be used to justify substantial one-off SST pricing. This follows from the ICER incremental cost per QALY willingness to pay thresholds where the SST QALY gains are sufficient, at even a $50,000 QALY cut-off, to support SST pricing in the millions of dollars. ICER has two options: (i) abandon the imaginary reference case methodology, which is the ICER core business model and would represent an ironic reversal, or (ii) attempt to bolt-on adaptations, possibly incorporating revised survivorship profiles using cure proportion modeling, that supports a modified imaginary reference case 'rescue' model for SSTs designed specifically to generate pricing recommendations that may be considered affordable.

Do Swiss community pharmacists address the risk of sexually transmitted infections during a consultation on emergency contraception? A simulated patient study

Objectives: Since 2002, Swiss community pharmacists have dispensed emergency contraception (EC) as pharmacist-only medicine ideally using the official Swiss protocol. Our study aimed to determine pharmacists’ resolution of an imaginary EC case, compliance with the protocol, and provision of information on the risk of sexually transmitted infections (STIs).Methods: We conducted a simulated patient study with 69 students who each visited a community pharmacy. The scenario started with the student requesting the ‘morning after pill’. Current practice was assessed using an online evaluation form adapted from the Medication-Related Consultation Framework. Descriptive and statistical analyses were carried out.Results: All pharmacists correctly identified that the person needed EC. All pharmacists used an EC protocol and asked on average 10.9 (standard deviation 0.68) of 11 compulsory EC assessment questions. In total, 93% of pharmacists addressed EC counselling items and 56% addressed the risk of STIs, mainly by mentioning that condoms offered the best protection (76%).Conclusions: Community pharmacists correctly issued the EC, complied with the dispensing protocol and used their professional judgement to ensure optimal EC use. There is nevertheless room for improvement regarding pharmacists’ STI counselling. Finally, the protocol’s STI section could be enriched with specific information to guide counselling.