Development of Nabla Fractional Calculus and a New Approach to Data Fitting in Time Dependent Cancer Therapeutic Study

The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will give us a better and more accurate outcome. This thesis consists of ve chapters. In the rst chapter, we give the history of the fractional calculus, and we present some basic de nitions and properties that are used in this theory. We de ne nabla fractional exponential and then nabla fractional trigonometric functions. In the second chapter, we concentrate on completely monotonic functions on R, and we introduce completely monotonic functions on discrete domain. The third chapter presents discrete Laplace N-transform table which is a great tool to nd solutions of -th order nabla fractional di erence equations. Furthermore, we nd the solution of nonhomogeneous up to rst order nabla fractional di erence equation using N-transform. In the fourth chapter, rst we give the de nition of Casoration for the set of solutions up to n-th order nabla fractional equation. Then, we state and prove some basic theorems about linear independence of the set of solutions. We focus on the solutions of up to second order nabla fractional di erence equation. We examine these solutions case by case namely, for the real and distinct characteristic roots, real and same, and complex ones. The fth chapter emphasizes the aim of this thesis. First, we give a vi brief introduction to parameter estimation with Gomperts and Logistic curves. In addition, we recall a statistical method called cross-validation for prediction. We state continuous, discrete, continuous fractional and discrete fractional forms of Gompertz and Logistic curves. We use the tumor growth data for twenty-eight mice for the comparison. These control mice were inoculated with tumors but did not receive any succeeding treatment. We claim that the discrete fractional type of sigmoidal curves have the best data tting results when they are compared to the other types of models

The Identification of The City on The Legibility and Wayfinding Concepts: A Case of Trabzon

The concept of wayfinding includes understanding the space and finding direction within the space. But as cities and architectural spaces grow and become more complex, visitors and locals of the space can find it difficult to find direction. For these reasons, for visitors who speak different languages, along with these elements, there is a need for well-designed information and direction-finding graphics and landmarks that have a universal quality. The aim of the study is to explain the concepts of wayfinding and way-finding, defined as “direction-finding” in the literature and to create awareness. Furthermore, to analyze the concept of wayfinding and the direction designs that aim to transform the cities that have become complex into more understandable spaces, through the city of Trabzon and to examine the problems of the city in this context and to make suggestions. In this study, Trabzon will be evaluated with the concepts of legibility and directability and the direction and information designs over the focal point, regions, edges, nodes, roads with which Kevin Lynch has defined the imageable, readable city. A survey was conducted to investigate the spatial information elements and legibility of   Trabzon city. Furthermore, to create awareness for other cities with similar problems

Design Approaches to Museum Open Spaces with User Evaluations

The concept of the museum today should be considered as a social communication platform, and museums should be designed by taking into account the interaction and harmony of their open and closed spaces with the immediate surroundings. This study emphasizes the importance of museums for the city and discusses design approaches to museum open spaces with examples of their effective use and an evaluation of the opinions of their users. In order to shed light on today's museum exterior design approaches, evaluations of the design setup of the museum open spaces were carried out on the basis of literature research and spatial experiences of the museum examples visited. In addition, using the content analysis method, by creating statements about usage, satisfaction level, and expectations, a questionnaire was planned and designed to be applied to a volunteer user group. According to the examples given and the survey data, museum open space designs were carried out. Four groups of factors - planning and design, social, functional and perceptual-having the greatest impact on visitor satisfaction were identified. The examples given include a discussion of museum open space facilities, along with commentary from the literature. For the evaluation of the users, a survey was conducted with 74 people. The survey asked about their satisfaction levels and their expectations in terms of museums and open spaces.  Since there was not chance to conduct face to face survey in pandemic conditions, the study was conducted that questioned the general qualifications. In addition to reaching the users visiting the museum were limited. When we look at the literature, multi-dimensional research has been carried out on museum architecture and design. However, no comprehensive study has been carried out on museum open spaces. Consequently, this study focused on the interaction between museum open spaces and visitors

Functional regression on remote sensing data in oceanography

The final publication is available at link.springer.comThe aim of this study is to propose the use of a functional data analysis approach as an alternative to the classical statistical methods most commonly used in oceanography and water quality management. In particular we consider the prediction of total suspended solids (TSS) based on remote sensing (RS) data. For this purpose several functional linear regression models and classical non-functional regression models are applied to 10 years of RS data obtained from medium resolution imaging spectrometer sensor to predict the TSS concentration in the coastal zone of the Guadalquivir estuary. The results of functional and classical approaches are compared in terms of their mean square prediction error values and the superiority of the functional models is established. A simulation study has been designed in order to support these findings and to determine the best prediction model for the TSS parameter in more general contexts.Peer ReviewedPostprint (author's final draft

The Atrial Fibrillation in Turkey: Epidemiologic Registry (AFTER)

Background: AFTER (Atrial Fibrillation in Turkey: Epidemiologic Registry) is a prospective,multicenter study designed with the aim of describing the prevalence and epidemiology ofAF practice in Turkey. This study aims to evaluate stroke risk in non-valvular atrial fi brillation(AF) and anticoagulant drug utilization within conformity to AF guidelines.Methods: Patients were recruited in 17 referral hospitals refl ecting all the population of7 geographical regions of Turkey. 2242 consecutive patients who had been admitted with AFon ECG were included in the study. 1745 of these patients, who had non-valvular AF, wereincluded in the statistical evaluation. Stroke risk was evaluated with the CHA2DS2-VASc score.Results: The average age of participants was determined to be 69.2 ± 11.5 years (56%female). Persistent-permanent AF was found to be the most common type of non-valvularAF (78%). The most common comorbid disorder was hypertension (73%). It was found thatoral anticoagulant therapy was used by 40% of all patients, 37% of whom had effective INR(2.0–3.0). Upon multivariate analysis, age was found to be the only independent predictorof stroke among the variables’ effects on thromboembolic events that created CHA2DS2-VAScabbreviations (OR 1.026, p < 0.001).Conclusions: These results suggest that stroke risk scores should be thoroughly heededbased on guidelines, and that anticoagulation must be applied according to their guidance

The Characteristic Clinical and Pathological Features of Incidental and Non-Incidental Papillary Microcarcinoma of the Thyroid

The incidence of papillary microcarcinoma (PMC) keeps raising due to fine needle aspiration (FNA) biopsies and the pathologic evaluation of thyroid specimens of cases operated for benign thyroid disorders. The files of 78 patients who underwent surgery between January 2006 and May 2013 in our department and were diagnosed with PMC were analyzed, retrospectively.Cases were grouped as incidental and non-incidental depending on the preoperative diagnosis. The diameter of the nodules in the preoperativeultrasonographic examination, pathological parameters such as tumor size, bilaterality, multifocality,and capsular invasion were found significantly high in non-incidental group(P<0.05). No significant difference was detected between the two groups’ age, sex, and vascular invasion.Preoperative radiologic examination by experienced radiologists and FNA performed for suspicious nodules may increase the rate of early and correct diagnosis. In our opinion, determining the most useful criteria for malignancy will help to detect incidental PMC in cases followed up for multinodular goiter

Spanish Validation of the 'User Reported Measure of Care Coordination' Questionnaire for Older People with Complex, Chronic Conditions

Older people with complex, chronic conditions often receive insufficient or inefficient care provision, and few instruments are able to measure their perception of care provision. The "User ReportedMeasure of Care Coordination" instrument has been satisfactorily used to evaluate chronic care provision and integration. The aim of this study is to validate this instrument in Spanish. Methods: The questionnairewas adapted and validated in two phases: translation and cultural adaptation of the questionnaire and psychometric property measurement. Study population were chronic care conditions patients. Results: A total of 332 participants completed test re-test as part of the questionnaire validation process. The final version of the questionnaire had 6 domains: Health andWell-being (D1), Health day to day (D2), Social Services (D3), Planned Care (D4), Urgent Care (D5), and Hospital Care (D6). Cronbach's alpha for the overall questionnaire was 0.86, indicating good internal consistency. When analyzing each domain, only Planned Care (D4) and Urgent Care (D5) had Cronbach's Alphas slightly lower than 0.7, although this could be related to the low number of items in each domain. A good temporal stabilitywas observed for the distinct subscales and items,with intraclass correlation coefficients varying from0.412 to 0.929 (p < 0.05). Conclusion: The adapted version of the "User ReportedMeasure of Care Coordination" into Spanish proved to be a practical tool for use in our daily practice and an efficient instrument for assessment of care coordination in chronic, complex conditions in older people across services and levels of care

Childhood-onset of primary Sjögren’s syndrome: phenotypic characterization at diagnosis of 158 children

Peer ReviewedPostprint (published version

Post-COVID-19 syndrome in patients with primary Sjögren's syndrome after acute SARS-CoV-2 infection

OBJECTIVES: To analyse the frequency and characteristics of post-COVID-19 syndrome in patients with primary Sjögren’s syndrome (pSS) affected by acute SARS-CoV-2 infection. METHODS: By the first week of April 2021, all centres included in the Big Data Sjögren Consortium were contacted asking for patients included in the Registry diagnosed with SARSCoV-2 infection according to the ECDC guidelines. According to the NICE definitions, symptoms related to COVID-19 were classified as acute COVID-19 (signs and symptoms for up to 4 weeks), ongoing symptomatic COVID-19 (presence of signs and symptoms from 4 to 12 weeks) and post-COVID-19 syndrome (signs and symptoms that continue for > 12 weeks not explained by an alternative diagnosis after a protocolized study). RESULTS: We identified 132 patients who were followed a mean follow-up of 137.8 days (ranging from 5 days to 388 days) after being diagnosed with COVID-19. In the last visit, 75 (57%) patients remained symptomatic: 68 (52%) remained symptomatic for more than 4 weeks fulfilling the NICE definition for ongoing symptomatic post-COVID-19, and 38 (29%) remained symptomatic for more than 12 weeks fulfilling the definition of post-COVID-19 syndrome. More than 40% of pSS patients reported the persistence of four symptoms or more, including anxiety/depression (59%), arthralgias (56%), sleep disorder (44%), fatigue (40%), anosmia (34%) and myalgias (32%). Age-sex adjusted multivariate analysis identified raised LDH levels (OR 10.36), raised CRP levels (OR 7.33), use of hydroxychloroquine (OR 3.51) and antiviral agents (OR 3.38), hospital admission (OR 8.29), mean length of hospital admission (OR 1.1) and requirement of supplemental oxygen (OR 6.94) as factors associated with a higher risk of developing post-COVID-19 syndrome. A sensitivity analysis including hospital admission in the adjusted model confirmed raised CRP levels (OR 8.6, 95% CI 1.33-104.44) and use of hydroxychloroquine (OR 2.52, 95% CI 1.00-6.47) as the key independent factors associated with an enhanced risk of developing post-COVID-19 syndrome. CONCLUSIONS: This is the first study that analyses the frequency and characteristics of post-COVID-19 syndrome in patients affected by a systemic autoimmune disease. We found that 57% of patients with pSS affected by COVID-19 remain symptomatic after a mean follow-up of 5 months. The risk of developing post-COVID-19 syndrome in patients who required hospitalisation was 8-times higher than in non-hospitalised patients, with baseline raised CRP levels and the use of hydroxychloroquine being independent risk factors for post-COVID-19.Peer ReviewedPostprint (published version

Characterization and outcomes of 414 patients with primary SS who developed haematological malignancies

Objective To characterize 414 patients with primary SS who developed haematological malignancies and to analyse how the main SS- and lymphoma-related features can modify the presentation patterns and outcomes. Methods By January 2021, the Big Data Sjögren Project Consortium database included 11¿966 patients fulfilling the 2002/2016 classification criteria. Haematological malignancies diagnosed according to the World Health Organization (WHO) classification were retrospectively identified. Results There were 414 patients (355 women, mean age 57¿years) with haematological malignancies (in 43, malignancy preceded at least one year the SS diagnosis). A total of 376 (91%) patients had mature B-cell malignancy, nearly half had extranodal marginal zone lymphoma (MZL) of mucosa-associated lymphoid tissue (MALT lymphoma) (n¿=¿197), followed by diffuse large B-cell lymphoma (DLBCL) (n¿=¿67), nodal MZL lymphoma (n¿=¿29), chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL) (n¿=¿19) and follicular lymphoma (FL) (n¿=¿17). Rates of complete response, relapses and death were 80%, 34% and 13%, respectively, with a 5-year survival rate of 86.5% after a mean follow-up of 8¿years. There were significant differences in age at diagnosis (younger in MALT, older in CLL/SLL), predominant clinical presentation (glandular enlargement in MALT lymphoma, peripheral lymphadenopathy in nodal MZL and FL, constitutional symptoms in DLBCL, incidental diagnosis in CLL/SLL), therapeutic response (higher in MALT lymphoma, lower in DLBCL) and survival (better in MALT, nodal MZL and FL, worse in DLBCL). Conclusion In the largest reported study of haematological malignancies complicating primary SS, we confirm the overwhelming predominance of B-cell lymphomas, especially MALT, with the salivary glands being the primary site of involvement. This highly-specific histopathological scenario is linked with the overall good prognosis with a 5-year survival rate of nearly 90%.Peer ReviewedPostprint (published version