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4. Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls

Author

Heuer, Karl and Sarikaya, Deniz

Subjects
Mathematics - Combinatorics, 05C63, 05C45, 05C75
Abstract

In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finite infinite graphs. For this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. In this paper we focus on conditions involving claws, nets and bulls as induced subgraphs. We extend Hamiltonicity results for finite claw-free and net-free graphs by Shepherd to locally finite graphs. Moreover, we generalise a classification of finite claw-free and net-free graphs by Shepherd to locally finite ones. Finally, we extend to locally finite graphs a Hamiltonicity result by Ryj\'{a}\v{c}ek involving a relaxed condition of being bull-free., Comment: 27 pages, 5 figures

Published
2020

5. Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws

Author

Heuer, Karl and Sarikaya, Deniz

Subjects
Mathematics - Combinatorics, 05C63, 05C45
Abstract

In this paper we extend a result about a sufficient condition for Hamiltonicity for finite graphs by Broersma and Veldmann to locally finite graphs. In order to do this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. The condition we focus on in this paper is in terms of forbidden induced subgraphs, namely being claw-free and a relaxation of being paw-free., Comment: 20 pages, 5 figures

Published
2020

13. How to Frame a Mathematician : Modelling the Cognitive Background of Proofs

Author

Fisseni, Bernhard, Sarikaya, Deniz, Schmitt, Martin, Schröder, Bernhard, Bueno, Otávio, Editor-in-Chief, Brogaard, Berit, Editorial Board Member, Chakravartty, Anjan, Editorial Board Member, French, Steven, Editorial Board Member, Dutilh Novaes, Catarina, Editorial Board Member, Centrone, Stefania, editor, Kant, Deborah, editor, and Sarikaya, Deniz, editor

Published
2019
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14. Introduction.

Author

Sarikaya, Deniz

Subjects
*BETWEENNESS relations (Mathematics), *MATHEMATICAL proofs, *PHILOSOPHY of mathematics, *SET theory, *MATHEMATICIANS
Abstract

This article introduces a special issue of Philosophical Investigations focused on Ludwig Wittgenstein's philosophy of mathematics and its connection to the philosophy of mathematical practice (PMP). The author acknowledges that while Wittgenstein is a highly influential philosopher, his work in the philosophy of mathematics is often overshadowed by his other writings. The special issue includes nine articles that cover various topics related to Wittgenstein's philosophy of mathematics and PMP. The articles explore Wittgenstein's practice-based approach to meaning, his views on set theory, his struggles with arithmetic and higher mathematics, and his critique of Cantorian set theory. The volume aims to deepen our understanding of mathematical practice, contribute to the discourse on Wittgenstein's philosophy of mathematics, and introduce Wittgensteinian ideas to the wider community of philosophers of mathematical practice. [Extracted from the article]

Published
2024
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18. Differentiation of Post-Polio Syndrome from Prior Poliomyelitis Sequela by Assessing Paraspinal Muscle Involvement in Magnetic Resonance Imaging.

Author

Topaloglu, Mahir, Sarikaya, Deniz, Peker, Ahmet, Senturk, Yunus Emre, Terlemez, Rana, Cetin, Burak Ugur, Oge, Ali Emre, and Ketenci, Aysegul

Subjects
*MAGNETIC resonance imaging, *POLIO, *LUMBAR pain, *MUSCLE weakness, *POSTPOLIOMYELITIS syndrome, *FATIGUE (Physiology)
Abstract

Background/Objectives: Post-polio syndrome (PPS) affects former polio patients, manifesting decades after initial infection with progressive symptoms like pain, fatigue, and muscle weakness. Diagnosis relies on the clinical criteria and exclusion of other probable causes. The purpose of this study is to determine the scope and new diagnostic value of magnetic resonance imaging (MRI) in identifying muscle involvement in PPS and distinguishing it from prior poliomyelitis (PPM). Methods: This study was approved by the Koç University Ethics Committee with Approval No. 2023.409.IRB2.090. Electronic medical archives from two academic institutions were searched for records tagged with ICD code B-91 for poliomyelitis sequalae. The resulting search query of 291 records was manually sorted for PPS and PPM, medical history, clinical examination findings, and lumbar MR images down to 32 patients. Two independent radiologists evaluated the paraspinal musculature in the MRIs using the Mercuri scale. Inter-rater agreement, comparison of the paraspinal musculatures between groups, and their relationship to leg involvement were assessed with the resulting data. Results: Inter-rater agreement was found to be almost perfect across all muscles, except for the multifidus muscle. When clinical examination findings were included for these muscles, quadratus lumborum (QL) degradation was found in both right-side (p = 0.017) and left-side (p = 0.002) leg involvement. Conclusions: QL muscle deterioration may serve as a diagnostic marker for PPS, potentially guiding lumbar pain treatment through rehabilitation. [ABSTRACT FROM AUTHOR]

Published
2024
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22. Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: Nets and bulls

Author

Heuer, Karl, Sarikaya, Deniz, Heuer, Karl, and Sarikaya, Deniz

Abstract

In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finite infinite graphs. For this we use topological circles within the Freudenthal compactification of a locally finite graph as infinite cycles. In this paper we focus on conditions involving claws, nets and bulls as induced subgraphs. We extend Hamiltonicity results for finite claw-free and net-free graphs by Shepherd to locally finite graphs. Moreover, we generalise a classification of finite claw-free and net-free graphs by Shepherd to locally finite ones. Finally, we extend to locally finite graphs a Hamiltonicity result by Ryjáček involving a relaxed condition of being bull-free.

Published
2023

23. THE POST-COVID 19 ERA, CHAT BOTS, AND THE HOMOGENIZATION OF EDUCATION: PLURALISM AS AN EPISTEMIC VIRTUE EXEMPLIFIED BY MATHEMATICS EDUCATION.

Author

Antonio Pérez-Escobar, José and Sarikaya, Deniz

Subjects
CHATBOTS, LANGUAGE models, VIRTUE epistemology, COVID-19 pandemic, MATHEMATICS education, ASYMPTOTIC homogenization, MATHEMATICS
Abstract

This paper aims to raise awareness about a potential harmful consequence of teaching adaptations due to the Covid-19 pandemic and advanced AI-powered chat bots in the context of large language models. As video lectures might undermine pluralism in mathematics, we argue that such developments could be harmful for mathematical practice and society at large. We argue that the mathematical undergraduate curriculum should not be too hard codified and formalized via an abuse of online teaching tools. In order to show why a plurality of research practices constitutes a great resource for mathematical progress, we will discuss a historical situation regarding the developments of the Tripos in Cambridge. We will also discuss analogies with economics and ideas on mathematical pluralism and productive ambiguity. Finally, we suggest that pluralism in education may be desirable in other fields too. [ABSTRACT FROM AUTHOR]

Published
2024

26. Targeting the blood-brain barrier disruption in hypertension by ALK5/ TGF-? : type I receptor inhibitor SB-431542 and dynamin inhibitor dynasore

Author

Atis, Muge, Akcan, Ugur, Altunsu, Deniz, Ayvaz, Ecem, Yilmaz, Canan Ugur, Sarikaya, Deniz, Temizyurek, Arzu, Ahishali, Bulent, Girouard, Helene, Kaya, Mehmet, Atis, Muge, Akcan, Ugur, Altunsu, Deniz, Ayvaz, Ecem, Yilmaz, Canan Ugur, Sarikaya, Deniz, Temizyurek, Arzu, Ahishali, Bulent, Girouard, Helene, and Kaya, Mehmet

Abstract

Introduction: In this study, we aimed to target two molecules, transforming growth factor-beta (TGF-beta) and dynamin to explore their roles in blood-brain barrier (BBB) disruption in hypertension. Methods: For this purpose, angiotensin (ANG) II-induced hypertensive mice were treated with SB-431542, an inhibitor of the ALK5/TGF-beta type I receptor, and dynasore, an inhibitor of dynamin. Albumin-Alexa fluor 594 was used to assess BBB permeability. The alterations in the expression of claudin-5, caveolin (Cav)-1, glucose transporter (Glut)-1, and SMAD4 in the cerebral cortex and the hippocampus were evaluated by quantification of immunofluorescence staining intensity.Results: ANG II infusion increased BBB permeability to albumin-Alexa fluor 594 which was reduced by SB431542 (P < 0.01), but not by dynasore. In hypertensive animals treated with dynasore, claudin-5 immunofluorescence intensity increased in the cerebral cortex and hippocampus while it decreased in the cerebral cortex of SB-431542 treated hypertensive mice (P < 0.01). Both dynasore and SB-431542 prevented the increased Cav-1 immunofluorescence intensity in the cerebral cortex and hippocampus of hypertensive animals (P < 0.01). SB431542 and dynasore decreased Glut-1 immunofluorescence intensity in the cerebral cortex and hippocampus of mice receiving ANG II (P < 0.01). SB-431542 increased SMAD4 immunofluorescence intensity in the cerebral cortex of hypertensive animals, while in the hippocampus a significant decrease was noted by both SB-431542 and dynasore (P < 0.01).Conclusion: Our data suggest that inhibition of the TGF beta type I receptor prevents BBB disruption under hypertensive conditions. These results emphasize the therapeutic potential of targeting TGF beta signaling as a novel treatment modality to protect the brain of hypertensive patients.

Published
2022
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28. Vorwort

Author

Löwe, Benedikt, Sarikaya, Deniz, History, Archeology, Arts, Philosophy and Ethics, and Centrum voor Logica en Wetenschapsfilosofie

Published
2022

29. Satzungen der DVMLG durch die Jahrzehnte

Author

Löwe, Benedikt, Sarikaya, Deniz, History, Archeology, Arts, Philosophy and Ethics, and Centrum voor Logica en Wetenschapsfilosofie

Published
2022

35. How to Frame a Mathematician

Author

Fisseni, Bernhard, Sarikaya, Deniz, Schmitt, Martin, Schröder, Bernhard, Centrone, Stefania, Kant, Deborah, Sarikaya, Deniz, and History, Archeology, Arts, Philosophy and Ethics

Subjects
Informatik, Mathematik, Germanistik, Philosophie
Abstract

Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the proofs are conducted; for the latter, we look at natural numbers and trees specifically.

Published
2019

39. Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free

Author

Kant, Deborah, Pérez-Escobar, José Antonio, and Sarikaya, Deniz

Abstract

This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorerapproach, because intuitions about mathematical objects are often unavailable for non-mathematicians (since they are sometimes hard to grasp even for mathematicians). This consideration is supported by a case study in set theory.

Published
2021
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40. The impact of exchange rate volatility on trade flows in large economies and developing countries

Author

Sarikaya, Deniz

Abstract

Meine Arbeit untersucht die Auswirkungen von Wechselkurs-Volatilität auf den bilateralen Handel zwischen den Handelsländerpaare in den letzten vier Jahrzehnten. Das Gravitationsmodell ist die Berechnungsmethode, um die Auswirkungen von Wechselkurs-Volatilität zu messen. Das Gravitationsmodell erlaubt neben der Wechselkurs-Volatilität, auch das Bestimmen anderer wirksamer Faktoren des gegenseitigen Handels: Mitglieder der WTO, der Distanzen zwischen den Ländern, regionale Handelsabkommen und so weiter. Die Analyse in dieser Arbeit beinhalten den multilateralen Widerstandseffekt, der durch van Wincoop (2003) präsentiert wird. Bei Langzeitanalyse zeigt Wechselkurs-Volatilität eine schwache negative Auswirkungen auf den Handel zwischen den Länder. Die Ergebnisse zeigen, dass im Vergleich die Industrieländer eine bessere Stabilität bei Wechselkurs-Volatilität besitzen, als die Schwellen- und Entwicklungsländern. Die Kurzzeitanalyse zeigt als alternative Messtechnik, eine ähnliche Wirkung wie die Langzeitanalyse. Meine analysierten Daten zeigen am Ende, dass der Abstand zwischen den Ländern eine stärkere Wirkung auf den bilateralen Handel hat, als die Wechselkurs-Volatilität im Vergleich. Mein Ergebnis unterstützt somit nicht die Annahme, das Wechselkurs-Volatilität einige starke negative Wirkung auf den bilateralen Handel habe., My thesis examines the effect of exchange rate volatility on bilateral trade between the trading country pairs for last four decades. The Gravity equation is the calculation method for measuring the effect of exchange rate volatility. Beside the volatility effect, Gravity equation also allows measuring other effective determinants on bilateral trade: membership of the WTO, the distance between the countries, regional trading agreements etcetera. The analyses in this thesis involve the multilateral resistance effect which is presented by van Wincoop (2003). The exchange rate volatility has a weak negative effect on trade between the country pairs in the long run analysis. The results show that developed economies has better resistance against the volatility effect compared to emerging and developing country economies. As an alternative measurement technique, the short term analysis shows the similar effect with long run analysis. At the end, my data analyses show that the distance between the countries has a stronger effect on bilateral trade compared to the exchange rate volatility effect. My results show that exchange rate volatility has no strong negative effect on bilateral trade.

Published
2016
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50. From Mathesis Universalis to Fixed Points and Related Set-Theoretic Concepts

Author

Jäger, Gerhard, Steila, Silvia, Bueno, Otávio, Editor-in-Chief, Brogaard, Berit, Editorial Board Member, Chakravartty, Anjan, Editorial Board Member, French, Steven, Editorial Board Member, Dutilh Novaes, Catarina, Editorial Board Member, Centrone, Stefania, editor, Negri, Sara, editor, Sarikaya, Deniz, editor, and Schuster, Peter M., editor

Published
2019
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