Operational Definition Research Articles

Is staging breast magnetic resonance imaging for invasive lobular carcinoma worthwhile?

Invasive lobular carcinoma (ILC) is challenging to stage accurately using mammography (MG) and ultrasound (US) with undiagnosed ipsilateral and contralateral cancer resulting in poor patient outcomes including return to surgery. Our institution employs routine staging breast MRI in ILC for this reason. However, increased time for further imaging/biopsies contributes to patient anxiety and potentially delays definite management. We aimed to quantify the frequency of staging MRI-detected additional lesions requiring biopsy or follow-up, the added cancer detection rate and MRI prompted change in surgical management. An observational study on staging breast MRI for newly diagnosed ILC at a tertiary Western Australian hospital from January 2019 to August 2022. Standardized 3T MRI protocol was performed, double read by unblinded fellowship-trained radiologists. Histopathology from biopsy, surgery, or first annual surveillance was the reference standard for additional MRI-detected lesions. One hundred ten MRI studies demonstrated 49 (45%) patients had at least one additional clinically significant MRI-detected lesion. Thirty-one patients had an additional ipsilateral lesion detected, of which 18 (58%) proved malignant; 14 (45%) multifocal and 4 (13%) multicentric ILC. Additional work-up of MRI-detected lesions averaged a 9-day delay to definitive surgery compared to patients with a negative or definitively benign MRI. MRI changed surgical planning in 11 of 110 cases from breast conservation surgery (BCS) to mastectomy and there were two contralateral cancers diagnosed. BCS reoperation rate was 11%. Staging MRI for ILC identifies clinically significant lesions in nearly half of patients, predominantly ipsilateral multifocal disease, without significant delay to definitive surgery.

Empty nest syndrome: A concept analysis.

Empty nest syndrome (ENS) is parents' experience to their children leaving home. Considering the lack of a clear definition of this concept and its context-based nature, this study aimed to define the ENS concept. A three-phase concept analysis using a hybrid model was used. In the theoretical (first) phase, a literature review was conducted using Scopus, WOS, PubMed, ProQuest, Irandoc, Research.idml, Magiran, and SID, with the search terms "empty nest syndrome," "aged," and "middle-aged," and their synonyms, with no time and language restrictions until the end of 2021. After the screening, 29 relevant articles entered the study. According to the findings of the first phase, the fieldwork (second) phase was directed using the qualitative content analysis approach, and semi-structured interviews were conducted with nine elderly and middle-aged individuals with an open-ended question. Results from both were included in the final (third) phase. The theoretical phase created an operational definition to guide the fieldwork phase. The fieldwork phase resulted in the emergence of six themes. The final analysis phase formulated a comprehensive definition of this concept: "ENS is a subjective phenomenon that occurs as a result of parents' reaction to their children leaving home." This transition from crisis to self-regaining includes the stages of mourning or resistance reaction, feelings of loss or passive behaviors, sublimation or impulsive behaviors, adaptation, and relief. It initiates with the last child's departure and continues until two years. Exploration of the concept of ENS can be the basis for designing a model or theoretical framework, devising measurement instruments for the concept and its consequences, and developing programs to increase the healthcare team's awareness to identify the problem and conduct appropriate preventive or therapeutic measures.

A single arm phase 2 clinical trial of YIV-906 with neoadjuvant concurrent chemo-radiation therapy in patients with locally advanced rectal cancer.

Pre-operative chemoradiation for rectal cancer is often associated with severe gastrointestinal (GI) toxicity which can interrupt, delay, and/or lead to termination of treatment. In this study, we evaluated whether the addition of YIV-906, a novel herbal medicine proven to reduce GI toxicity associated with chemotherapy could also reduce GI side effects during standard pre-operative capecitabine and pelvic radiation therapy (RT) in the neoadjuvant setting for the treatment of locally advanced rectal cancer. This single arm clinical study enrolled 24 patients between Dec 23, 2014-Sep 17, 2018 at Smilow Cancer Hospital, a comprehensive cancer center at Yale New Haven Hospital. All patients were age ≥18 years, Eastern Cooperative Oncology Group 0-1 and with histologically confirmed T3-T4 and N0-N2, M0 adenocarcinoma of the rectum. Median follow-up was 61.9 months. All patients received concurrent pelvic external beam RT (50.4 Gy in 28 fractions), YIV-906 (taken orally 800 mg twice daily on days 1-4 of RT each week), and oral capecitabine delivered in a neo-adjuvant fashion, followed by definitive surgery. Toxicity was assessed weekly during radiation and until acute symptoms resolved and then at 28 days, 4 months, 7 months and 10 months. Toxicities were graded in accordance with Common Terminology Criteria for Adverse Events (CTCAE) version 4.0. At the time of surgery, 4 patients (16.7%) had a complete or near-complete response. At a median follow-up of 61.9 months, the mean overall survival (OS) of our patient cohort was 74.9 months [95% confidence interval (CI): 67.3-82.5]. The estimated 5-year OS was 82.0%. We observed 0% acute grade 4 toxicities, and only two cases of acute grade 3 diarrhea (8.3%). The addition of YIV-906 to capecitabine based chemoradiation for locally advanced rectal cancer led to reduced rates of GI toxicity compared to historical controls, in particular grade 3 or greater diarrhea. These findings suggest YIV-906 should be evaluated in a randomized clinical trial to further assess potential reductions in the toxicity profile of chemoradiation for GI cancers.

Conceptual and Operational Definitions of the “Narrative” Concept (on the Issue of Automated Extraction of Narratives from Big Data)

Conceptual and Operational Definitions of the “Narrative” Concept (on the Issue of Automated Extraction of Narratives from Big Data)

Evaluasi Penyelesaian Temuan Pemeriksaan yang Tidak Dapat Ditindaklanjuti (TPTD) Hasil Pemeriksaan Inspektorat Jenderal

This study aims to evaluate the implementation of the TPTD settlement process from the Inspectorate General examination results compared to the applicable TPTD guidelines. The study was conducted at the Inspectorate General of the Ministry of Health. This research uses a case study research strategy with a qualitative descriptive data analysis method. The data sources used were obtained from interviews and documentation. The results showed that the implementation of the settlement has followed the applicable TPTD guidelines but it is necessary to update the follow-up guidelines and make technical follow-up instructions for the results of supervision or TPTD special guidelines that explain the operational definition of TPTD criteria regarding benchmarks and document limits from authorized agencies that must be met as TPTD requirements, work steps regarding the TPTD proposal mechanism from the work unit, discussion and determination of TPTD by the Inspectorate General, as well as the format of submitting TPTD proposals along with supporting data that must be completed. Recommendations of audit results that become TPTD due to improper provision of recommendations The Inspectorate General can carry out the development of APIP competence of the Inspectorate General on an ongoing basis. The findings decided by TPTD but seen from the follow-up carried out are not timely or protracted, it is necessary to monitor the follow-up carried out by the Inspectorate General every month and be actively involved in maintaining the time commitment. Keywords: Findings, follow-up Inspectorate General, TPTD, recommendations

Safeguarding adults: A concept analysis

AbstractAimsThis article aimed to examine the concept of safeguarding adults and establish an operational definition for application to practice, research and policy.DesignRodgers' evolutionary and inductive method of concept analysis was used.Data SourcesA systematic search was conducted across four electronic databases, CINAHL, PsycINFO, Scopus and PubMed, covering the period from January 2014 to May 2023. This systematic database search aimed to gather a broad spectrum of research and scholarly literature to inform and support the concept analysis. A total of 10 peer‐reviewed articles were reviewed using a data chart to identify the context, definitions, antecedents, attributes and consequences of safeguarding adults.ResultsThe analysis of the included articles helped to develop a better understanding of safeguarding adults by offering a practical operational definition tailored to the specific needs of practising nurses. The implications for practice, research and policy are discussed, highlighting the potential for improving the quality of care and ensuring the well‐being of adults at risk of abuse.ConclusionBy employing Rogers' evolutionary concept analysis method, we developed a deeper insight into safeguarding adults in health care. A synthesis of literature revealed the intricate layers and adaptations within safeguarding practices. This concept analysis lays the groundwork for future research, policy development and educational initiatives, enhancing the well‐being and safety of adults at risk of abuse within care.ImpactBy undertaking a concept analysis of the term safeguarding adults' nurses can be more prepared to engage in and reinforce the key principles of safeguarding adults, providing guidance to ensure the protection and well‐being of adults at risk of abuse.Patient or Public ContributionNot applicable.What this Paper Contributes to the Wider Body of KnowledgeThis concept analysis helps to define and clarify the conceptual term ‘safeguarding adults’ promoting a shared understanding of the key components of adult protection and providing a comprehensive framework for assessment and management of adults at risk of abuse in this field of practice.

Development of a non-standard system for simplifying boolean functions

The object of this study is models of low-power digital logic circuits. The problem being solved is the effectiveness of the technique for simplifying Boolean functions to obtain optimal structures of logic circuits. A new theorem of a non-standard system of simplification of Boolean functions has been formulated, according to which in order to obtain a minimal function it will suffice to perform all non-redundant operations of simple and/or super-gluing of variables, which ultimately provides a minimal function in the main basis without using an implicant table. Thus, the problem of simplifying Boolean functions to the simplest normal equivalent is solved in one step. The interpretation of the result is that the properties of 2-(n, b)-design combinatorial systems make it possible to reproduce the definition of logical operations of super-gluing variables, to represent logical operations in a different way, and vice versa. This, in turn, ensures the establishment of the locations of equivalent transformations on the binary structure of the truth table and the implication of a systematic procedure for simplifying Boolean functions by an analytical method. Special feature of the results is that unambiguous identification of the locations of equivalent transformations is possible even when different intervals of the Boolean space containing the 2-(n, b)-design systems have common modules. It has been experimentally confirmed that the non-standard system improves the efficiency of simplifying Boolean functions, including partially defined ones, by 200–300 % compared to analogs. In terms of application, a non-standard system for simplifying Boolean functions will ensure the transfer of innovations to material production: from conducting fundamental research, expanding the capabilities of digital component design technology to organizing serial or mass production of novelties

Leiomyomatosis: A Rare Case of Mistaken Identity

Abstract: Diffuse uterine leiomyomatosis (DUL) is a rare benign uterine pathology that is often misdiagnosed as uterine leiomyomas. We present a case of a woman with abnormal uterine bleeding treated with multiple medical therapies without symptomatic relief. She underwent two surgeries, almost a year apart, with the histopathologic diagnosis of leiomyomas. After numerous failed attempts at medical and surgical treatments, the patient requested definitive surgery and underwent a robotic-assisted laparoscopic hysterectomy. Histopathologic analysis of the entire uterine specimen confirmed diffuse uterine leiomyomatosis. Case Report: A 31-year-old female was referred to our office with a history of abnormal uterine bleeding and heavy menstrual bleeding who failed hormonal therapies. Levonorgestrel-releasing intrauterine devices were inserted at two different times and were expelled due to heavy menses. Pelvic magnetic resonance imaging reported leiomyomas. The patient underwent hysteroscopy and a robotic-assisted myomectomy. Pathology revealed leiomyomas. Seven months after her first surgery, her bleeding recurred, and the patient became severely anemic, requiring hospitalization and transfusion of 2 units of packed RBCs. Over a year later, the patient underwent a second hysteroscopic and robotic myomectomy after failed medical therapies of tranexamic acid, progesterone medication, and gonadotropin-releasing hormone antagonist with minimal symptom relief. Her quality of life suffered tremendously due to ongoing AUB-HMB. After seven months, the patient requested definitive surgical therapy and underwent a robotic-assisted laparoscopic hysterectomy. Pathology reported diffuse uterine leiomyomatosis. Diffuse uterine leiomyomatosis is a rare benign uterine pathology that is often misdiagnosed as uterine leiomyomas. Early diagnosis of DUL is challenging and often inconclusive. Less than 50 diffuse uterine leiomyomatosis cases have been reported in the literature. The myometrium in DUL is almost entirely replaced by numerous ill-defined benign smooth muscle tumors. MRI offers mapping of the size, site, and distribution of leiomyomas, but findings are difficult to differentiate from DUL. The pathophysiology of DUL development remains poorly understood, with patients frequently complaining of abnormal uterine bleeding, heavy menstrual bleeding, fertility issues, and dysmenorrhea. DUL is often misdiagnosed as leiomyomas or adenomyosis clinically, given the similarity in manifestations. Leiomyomatosis is histologically characterized by the proliferation of smooth muscle cells forming fascicles and nodules, which blend with normal myometrium tissue. Hysterectomy is the definitive treatment of DUL, with this case report demonstrating the close similarity between the two.

Language-based capabilities to conceptualise linguistic justice

Abstract This article proposes an application of the capability approach (CA) within linguistic justice, adopting a capability-based approach. The aim is to break down the concept into language-based capabilities associated with public goods, which can be evaluated through qualitative or quantitative methods, aligning with policy cycle models. The objective is to deconstruct the abstract notion of linguistic justice into manageable components, namely language-based capabilities, making it amenable to scrutiny through policy analysis. Language-based capabilities are capabilities linked to public goods and services that inherently require a language for conversion into functioning. The state plays a crucial role as a conversion enabler through fair and effective language policies. This breakdown into language-based capabilities facilitates the identification of individual strategies, making the evaluation of language policies easier. Such an approach enables an examination of the policymaking process, including its efficacy, shortcomings, and opportunities for improvement. The ultimate goal is to translate a highly normative approach into an operational definition, further breaking it down into measurable indicators, thereby advancing the field.

Foundational concepts of collaborative practice with parents in occupational therapy for children.

In occupational therapy for children, collaborative practice with parents is crucial for meaningful family-centred interventions, yet it remains undefined and inconsistently addressed. This study aimed to establish foundational concepts for collaborative practice with parents in occupational therapy for children in progressing the field with a universal description. This paper encompasses the second dataset of a larger scoping review and a preliminary validation of findings by an advisory panel. Data were gathered from indexed sources on collaborative practice with parents in occupational therapy for children (ages 0-10) using MedLine, PsychInfo, ERIC, Embase, OTSeeker, Scopus, and ProQuest Central. Data were extracted, charted, and descriptively analysed by paired independent reviewers. The Joanna Briggs Institute Manual and the Preferred Reporting Items for Systematic Reviews and Meta-Analysis-extension for Scoping Reviews were used. A draft definition of collaborative practices, developed based on preliminary review findings and an operational definition, was validated by an advisory panel of 13 experienced Australian occupational therapists, whose input was integrated into a final, comprehensive description of collaborative practice. The scoping review encompassed 299 sources, revealing three major components of collaborative practice: 'collaborative practice aims', 'parent-therapist partnership', and 'strategies for collaboration'. The advisory panel endorsed the draft definition, confirmed its professional relevance, and suggested some modifications. The major outcome of this study is an evidence-based and discipline-specific preliminary description of collaborative practice with parents in occupational therapy for children. This description provides a common language and foundational concepts for the future development of a collaborative practice framework to guide practice and research. Future studies can explore specific components, exploring their mechanisms and significance. Further expanded validation is required, incorporating the perspectives of a wider community of occupational therapists and families to enhance the description's applicability.

Leadership as a determinant of need fulfillment: implications for meta-theory, methods, and practice.

Of all the most prominent business concepts (e.g., DE&I, employee well-being, employee engagement, organizational culture, etc.) none rivals leadership in terms of public interest and annual monetary investment. Despite the obvious importance of leadership as a determinant of many important outcomes, the concept of leadership has been surprisingly hard to pin down, lacking consensus as to its precise meaning. As numerous authors introduce ever more constructs (e.g., servant leadership, toxic leadership, sustainable leadership, transformational leadership, etc.), the leadership concept has become emblematic of the problem of construct proliferation. Like the related fields of employee engagement, subjective well-being, and organizational culture, the leadership field is in desperate need of a clearly articulated meta-theory to house its many constructs, allowing theory and measurement to build up instead of continuing to pile up. This paper argues for grounding the concept of leadership within the psychological literature on human needs. In reviewing the leading definitions of leadership in the literature we find that they are reducible to a core set of follower needs that can be facilitated or inhibited by leaders. We propose that there is substantial value in adopting a comprehensive needs-based taxonomy over current approaches. We consider the impact of setting the concepts of leadership within existing need constructs for each of the following: (a) theory, especially the development of leadership frameworks and particularly how the concept of leadership relates to the concepts of organizational culture, employee well-being, and employee engagement; (b) methods, including the value of applying a comprehensive, structured model; and (c) practice, where we emphasize the practical advantages of clear operational definitions.

A conceptual framework for measuring and improving the resilience of biosecurity systems

Abstract Resilient systems can absorb and recover from disturbances and adapt to changed conditions to maintain system functionality. Uncertainty about the meaning of resilience and the attributes it requires has limited the application of resilience thinking in biosecurity. However, considering increasing pressures from trade, travel and climate change, enhancing the resilience of biosecurity systems is likely to be critical to reduce the impacts of pests and diseases on economies, societies and environments. Here we provide a pathway for resilience thinking into risk management. Based on a literature review we discuss its benefits, develop an operational definition of resilience for biosecurity systems and identify the fundamental attributes that support resilience. We show that resilient biosecurity systems can anticipate disturbances, cope with low‐probability high‐impact events and adapt to new and changing circumstances. The status of biosecurity system resilience can be measured using evaluative rubrics, which give decision‐makers an overall performance rating and insight into system weaknesses. General measures, objective functions and simulation approaches are potential avenues for quantifying biosecurity system resilience in practice. Policy implications: Adopting resilience thinking into biosecurity risk management has the potential to reduce the damages caused by invading pests and diseases. If resilience thinking is used alongside traditional risk analysis, then regulators can more effectively address and prepare for the systemic consequences of high‐impact incursions and outbreaks of pests and diseases, which are unpredictable, low‐probability events. However, the design of resilience‐enhancing measures should be guided by economic principles and consider the rate of return of these measures over time.

Factors influencing engagement in pelvic floor muscle exercise following radical prostatectomy: A scoping review

AbstractInconsistent engagement in pelvic floor muscle exercise (PFME) among patients with prostate cancer (PC) following radical prostatectomy may have contributed to varying effectiveness in improving urinary incontinence across studies. Identifying factors influencing engagement can help develop effective interventions to maximize participation, enhance urinary function and improve quality of life (QoL). This scoping review aims to systematically search for factors influencing PFME engagement among post radical prostatectomy patients managing urinary incontinence. Eligible publications in English were identified from various databases, including PubMed, CINAHL, ProQuest, PsycINFO and Scopus. A health science librarian was consulted to assist in formulating search terms, encompassing PC, PFME terms and influencing factors terms. We employed Colandrapp™ for data extraction, focusing on key themes such as study characteristics, PFME education and training, recommended sessions, engagement rates and factors influencing PFME engagement following radical prostatectomy. Results were presented in tables and supplemented by a narrative discussion addressing gaps in research knowledge. The synthesis drew from a diverse body of literature, blending quantitative and qualitative approaches, to contribute to a comprehensive understanding of PFME engagement factors. Twelve papers, based on 10 studies published between 2011 and 2018, met our inclusion criteria. The reviewed studies primarily employed longitudinal quantitative designs, except for one study that utilized a mixed‐method design. Only three studies incorporated theories to guide the selection of potential factors influencing PFME engagement. The factors examined across the reviewed studies encompassed aspects related to the patient–partner relationship, patient's action control, planning (dyadic or individual), self‐efficacy, perceived urinary incontinence and the patient–provider relationship. We observed conflicting findings regarding the factors influencing PFME engagement across studies. Our review underscores the importance of theory‐informed studies using rigorous methodology and precise theoretical and operational definitions of potential factors. Such studies can help pinpoint the most influential factors to enhance PFME engagement and, ultimately, improve symptoms and QoL for PC patients. The scoping review also showed critical implications for nursing practice. Nurses should develop individualized and culturally sensitive interventions, integrate health behaviour change theories, assess patient–partner relationships and action control and consider intention's mediating role in the enhancement of PFME engagement following radical prostatectomy.

Early Outcomes of Hirschsprung's Disease after Definitive Surgery: A Ten-Year Experience.

This study aimed to examine the characteristics of Hirschsprung's Disease (HD) in patients aged<18 who underwent surgical procedure at Dr. Zainoel Abidin (RSUDZA) General Hospital, Banda Aceh, Indonesia, between January 2010 and December 2020. This retrospective study collected and analyzed data from medical records of 18-yearold or younger children (n = 180) diagnosed with HD at RSUDZA. The surgical procedures included the Duhamel procedure, Soave procedure, the Soave Transanal Endorectal Pull-through (TEPT) procedure, and the Swenson TEPT procedure. Early outcomes of the surgery were then compared between males and females. The comparrative analysis was determined based on Chisquare analysis, where p&#60; 0.05 was considered significant. There were 111 (61.7%) male patients and 69 (38.3%) female patients, with a mean age of 15.2 months. The Soave TEPT is the most frequently performed procedure (91.7%). Emerging clinical manifestations include constipation (176; 97.8%) and soiling (171; 95%). Preoperative barium enema and postoperative pathological examination confirmed that almost all patients (99.4%) had an aganglionic segment confined to the rectosigmoid area. The average length of operation was 69.7 ± 65 minutes and average bleeding time was 5.4 ± 34 mL. The average discharge time was 3.3 ± 73.3 days. No significant difference was found in post-surgery complications between males and females (p&#60;0.5). The immediate complications were not associated with surgical methods (p = 0.83). Our descriptive study has suggested the Soave TEPT technique as appropriate to manage HD.

The expanding role of radiation oncology across the prostate cancer continuum.

Radiotherapy is used in the treatment of prostate cancer in a variety of disease states with significant reliance on imaging to guide clinical decision-making and radiation delivery. In the definitive setting, the choice of radiotherapy treatment modality, dose, and fractionation for localized prostate cancer is determined by the patient's initial risk stratification and other clinical considerations. Radiation is also an option as salvage therapy in patients with locoregionally recurrent disease after prior definitive radiation or surgery. In recent years, the role of radiation has expanded for patients with metastatic disease, including prostate-directed radiotherapy in de novo low volume metastatic disease, metastasis-directed therapy for oligorecurrent disease, and palliative management of symptomatic metastases in the advanced setting. Here we review the expanding role of radiation in the treatment of prostate cancer in the definitive, locoregionally recurrent, and metastatic settings, as well as highlight the role of imaging in clinical reasoning, radiation planning, and treatment delivery.

Anorectal malformation and Hirschsprung’s disease: a cross-sectional multicentre comparison of quality of life and bowel function to a healthy population

PurposeChildren with anorectal malformation (ARM) and Hirschsprung’s disease (HD) often experience bowel symptoms into adulthood, despite definitive surgery. This study evaluates the quality of life (QOL) and bowel functional outcome...

Characteristics and Clinical Features of Anorectal Malformations Without Fistula: A Systematic Literature Review

Anorectal malformation (MA) without fistula is a form of congenital abnormality that is often found in newborn babies. This study aims to identify the characteristics and clinical features of MA without fistula based on the latest scientific evidence. A systematic search was conducted on the PubMed, Scopus, and Web of Science databases using relevant keywords. Inclusion criteria included observational studies reporting the characteristics and clinical features of MA without fistula in humans. Two independent researchers conducted study selection, data extraction, and study quality assessment using the JBI Critical Appraisal Checklist tool. A total of 25 studies (2018-2024) involving 1548 MA patients without fistula met the inclusion criteria. The majority of patients were male (62%). The average age at diagnosis is 2 days. The most frequently reported clinical symptoms were absence of anus (100%), abdominal distension (78%), and vomiting (65%). The most common classification of MA without fistula was perineal (45%), followed by vestibular (30%) and cloacal (25%). The most frequently performed definitive surgery was perineal anoplasty (55%), followed by posterior sagittal anorectoplasty (PSARP) (35%) and laparoscopic-assisted anorectoplasty (10%). The most frequently reported postoperative complications were anal stenosis (15%), surgical wound infection (10%), and rectal prolapse (5%). MA without fistula is more common in male babies. The main clinical symptoms are absence of anus, abdominal distension, and vomiting. The perineal classification is the most common. Perineal anoplasty is the most frequently performed definitive surgery. Post-operative complications that need to be watched out for are anal stenosis, surgical wound infection, and rectal prolapse.

Community resilience placed at the service of the climate-migration-conflict nexus understanding

In the frame of the so-called climate-migration-conflict nexus (CMCN), the potential correlation between these three dimensions has been widely explored. Furthermore, the literature calls for efforts to focus on responding to the impacts on society of this nexus through the development of forms of adaptation, mitigation and resilience. In particular, in the context of CMCN, the concept of community resilience has not received sufficient attention. More generally, this concept has not been the subject of homogeneous definitions such that it can be adequately operationalised in the analysis of CMCN. Bearing in mind the findings from CMCN research and referring to the existing literature on community resilience, we intend to make a theoretical contribution to the debate on this latter concept. The results will take the shape of an operational definition of community resilience that can also be applied in the context of CMCN. Consequently, this reflection may also contribute to overcoming the linear cause-effect approach that has been the subject of the majority of studies on CMCN, by taking into consideration a wider broader spectrum of geographical, political, social, cultural, demographic and economic variables.

Frege on Identity and Identity Statements: 1884/1903

ABSTRACT In this essay, I first solve solve a conundrum and then deal with criteria of identity, Leibniz's definition of identity and Frege's adoption of it in his (failed) attempt to define the cardinality operator contextually in terms of Hume's Principle in Die Grundlagen der Arithmetik. I argue that Frege could have omitted the intermediate step of tentatively defining the cardinality operator in the context of an equation of the form ‘NxF(x) = NxG(x)'. Frege considers Leibniz's definition of identity to be purely logical, although without saying why it is in line with his logicist project. I argue that the universal criterion of identity that Frege takes from Leibniz's definition and the specific criterion of identity for cardinal numbers embodied in Hume’s Principle (namely equinumerosity) work hand in hand in the tentative contextual definition of the cardinality operator. Yet the interplay between the two criteria is powerless to prevent the emergence of the Julius Caesar problem, let alone suggests how it could be solved. The final explicit definition of the cardinality operator that Frege sets up still rests on the identity criterion of equinumerosity since cardinal numbers are defined as equivalence classes of that relation.

Action of the Axial U(1) Non-Invertible Symmetry on the ’t Hooft Line Operator: A Lattice Gauge Theory Study

Abstract We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the ’t Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact scalar boson, the “QED axion”. For the gauge invariance, the simple ’t Hooft line operator, which is defined by a line integral of the dual $U(1)$ gauge potential, must be “dressed” by the scalar and $U(1)$ gauge fields. A careful consideration on the basis of the anomalous Ward–Takahashi identity containing the ’t Hooft operator with the dressing factor and a precise definition of the symmetry operator on the lattice shows that the symmetry operator leaves no effect when it sweeps out a ’t Hooft loop operator. This result appears inequivalent with the phenomenon concluded in the continuum theory. In an appendix, we demonstrate that the half-space gauging of the magnetic $\mathbb {Z}_N$ 1-form symmetry, when formulated in an appropriate lattice framework, leads to the same conclusion as above. A similar result is obtained for the axion string operator.