When Self-Generated Gradients interact with Expansion by Cell Division and Diffusion. Analysis of a Minimal Model

We investigate a minimal model for cell propagation involving migration along self-generated signaling gradients and cell division, which has been proposed in an earlier study. The model consists in a system of two coupled parabolic diffusion-advection-reaction equations. Because of a discontinuous advection term, the Cauchy problem should be handled with care. We first establish existence and uniqueness locally in time through the reduction of the problem to the well-posedness of an ODE, under a monotonicity condition on the signaling gradient. Then, we carry out an asymptotic analysis of the system. All positive and bounded traveling waves of the system are computed and an explicit formula for the minimal wave speed is deduced. An analysis on the inside dynamics of the wave establishes a dichotomy between pushed and pulled waves depending on the strength of the advection. We identified the minimal wave speed as the biologically relevant speed, in a weak sense, that is, the solution propagates slower, respectively faster, than the minimal wave speed, up to time extraction. Finally, we extend the study to a hyperbolic two-velocity model with persistence

The Understanding of Tasawwuf and Tariqat in al-Birgiwi

Al-Birgiwi is considered one of the most notable scholars in a series of disputes occurred between sufis and ulema in the 16th century of Ottoman Empire. His views about innovation (bid. at), esoteric Sufism and tariqats in those discussions in which he adopted a rather strict and strong language were assessed and criticized by a number of authors. These assessments generally comprise that Mehmed Birgivi (d. 981/1573) disregarded all traditions and customs in the society and was affected by salafism, but it is conspicuous that most of these opinions and claims about his approaches are either inaccurate or inadequate as a result of the lack of the interest in obtaining his viewpoint as a whole from his books in connection with the topics in question. So, we observe that those evaluations portray his opinions differently when we investigate them in his related books. In this paper, we argue al-Birgiwi's viewpoint on Tasawwuf and Tariqats through his works and analyze some opinions and claims in this regard.https://doi.org/10.7596/taksad.v6i4.105

Collective movement in Dictyostelium discoideum and other species : modelling, analysis and simulations

Cette thèse s'inscrit dans le domaine de la modélisation du mouvement cellulaire collectif et de l'analyse de phénomènes de propagation dans ces modèles. Le point de départ de cette thèse est la modélisation mathématique d'une expérience, où une colonie de Dictyostelium discoideum parvient à échapper l'hypoxie grâce à un remarquable comportement collectif. Il est montré que la consommation d'oxygène conduit à des gradients d'oxygène auto-générés, qui servent d'indicateurs de navigation aux cellules et déclenchent un mouvement collectif vers des zones de teneur en oxygène plus élevée. Le mouvement se maintient sur des larges échelles à travers la consommation permanente d'oxygène par les cellules. Par un modèle élémentaire EDP, que nous désignons par modèle "Se déplacer ou Se diviser" (Go or Grow en anglais), nous montrons que la combinaison de la division cellulaire et de l'aérotactisme joue un rôle crucial dans ce comportement collectif. En particulier, cette approche conduit à une formule explicite de la vitesse de propagation. Nous conduisons ensuite une analyse mathématique du modèle "Se déplacer ou Se diviser", qui inclut notamment un résultat d'existence et d'unicité du modèle localement en temps, une analyse de la dynamique intérieure de la population en propagation, ainsi qu'une caractérisation faible du comportement de propagation asymptotique. Suite à ce travail, nous nous interrogeons sur les conditions sous lesquelles une population cellulaire peut se propager, en générant leur propre gradient de signalisation. Nous mentionnons des résultats antérieurs dans la littérature et discutons de divers scénarios de modélisation, qui conduisent à ce type de phénomènes de propagation. Ensuite, nous proposons une approche pour concevoir des schémas numériques bien équilibrés pour des ondes progressives dans des modèles cinétiques et paraboliques. Cette approche combine une estimation de la vitesse de propagation instantanée, ainsi que des techniques documentées dans la littérature pour concevoir des schémas bien équilibrés. Enfin, nous étudions un modèle "Se déplacer ou Se diviser" stochastique et individu-centré, qui se fonde sur une simple règle "Se déplacer ou Se diviser". Nous conjecturons une limite en large population, qui peut être vu comme un modèle "Se déplacer ou Se diviser" alernatif, et étudions numériquement les lignées ancestrales des particules. Ainsi, nous proposons un point de vue parallèle sur les dynamiques intérieures. Le modèle "Se déplacer ou Se diviser" alternatif est analysée et nous donnons des résultats préliminaires sur le comportement asymptotique de la propagation.This thesis is concerned with the modeling of collective cell movement and the analysis of spreading phenomena arising in these models. The starting point of the thesis is the mathematical modeling of an experiment, where a colony of Dictyostelium discoideum is able to escape hypoxia through a remarkable collective behavior. It is shown that oxygen consumption leads to self-generated oxygen gradients, which serve as directional cues and trigger a collective movement towards higher oxygen regions. This movement is sustained over large scales by the perpetual consumption of oxygen by the cells. Through an elementary PDE model, the so-called Go or Grow model, we show that the combination of cell division and aerotaxis plays a key role in this collective behavior. In particular, this approach leads to an explicit formula for the propagation speed. We carry out a thorough mathematical analysis of the Go or Grow model, including a result of existence and uniqueness locally in time of the model, an analysis of the inside dynamics of the propagating population, as well as a weak characterization of the asymptotic spreading behavior. Following the aforementioned investigation, we address the question under which circumstance a cell population may propagate, by generating their own signaling gradients. We do a survey on existing results in the literature and discuss various modeling scenarios, which lead to this type of propagation phenomena. Then, we propose an approach to design well-balanced numerical schemes for traveling waves in kinetic and parabolic models. The approach combines an estimate of the instantaneous spreading speed with techniques taken from the literature to design well-balanced schemes. Finally, we study a stochastic individual-based Go or Grow model, which is based on a simple Go or Grow rule. We conjecture the large population limit, which can be seen as an alternative Go or Grow model, and investigate numerically the ancestral lineages of particles. This leads to an alternative viewpoint on the inside dynamics. The alternative Go or Grow model is analyzed and we give preliminary results estimating the asymptotic behavior of the spreading

Mouvement collectif chez Dictyostelium discoideum et autres espèces. Modélisation, analyse et simulations

This thesis is concerned with the modeling of collective cell movement and the analysis of spreading phenomena arising in these models. The starting point of the thesis is the mathematical modeling of an experiment, where a colony of Dictyostelium discoideum is able to escape hypoxia through a remarkable collective behavior. It is shown that oxygen consumption leads to self-generated oxygen gradients, which serve as directional cues and trigger a collective movement towards higher oxygen regions. This movement is sustained over large scales by the perpetual consumption of oxygen by the cells. Through an elementary PDE model, the so-called Go or Grow model, we show that the combination of cell division and aerotaxis plays a key role in this collective behavior. In particular, this approach leads to an explicit formula for the propagation speed. We carry out a thorough mathematical analysis of the Go or Grow model, including a result of existence and uniqueness locally in time of the model, an analysis of the inside dynamics of the propagating population, as well as a weak characterization of the asymptotic spreading behavior. Following the aforementioned investigation, we address the question under which circumstance a cell population may propagate, by generating their own signaling gradients. We do a survey on existing results in the literature and discuss various modeling scenarios, which lead to this type of propagation phenomena. Then, we propose an approach to design well-balanced numerical schemes for traveling waves in kinetic and parabolic models. The approach combines an estimate of the instantaneous spreading speed with techniques taken from the literature to design well-balanced schemes. Finally, we study a stochastic individual-based Go or Grow model, which is based on a simple Go or Grow rule. We conjecture the large population limit, which can be seen as an alternative Go or Grow model, and investigate numerically the ancestral lineages of particles. This leads to an alternative viewpoint on the inside dynamics. The alternative Go or Grow model is analyzed and we give preliminary results estimating the asymptotic behavior of the spreading.Cette thèse s’inscrit dans le domaine de la modélisation du mouvement cellulaire collectif et de l’analyse de phénomènes de propagation dans ces modèles.Le point de départ de cette thèse est la modélisation mathématique d’une expérience, où une colonie de Dictyostelium discoideum parvient à échapper l’hypoxie grâce à un remarquable comportement collectif. Il est montré que la consommation d’oxygène conduit à des gradients d’oxygène auto-générés, qui servent d’indicateurs de navigation aux cellules et déclenchent un mouvement collectif vers des zones de teneur en oxygène plus élevée. Le mouvement se maintient sur des larges échelles à travers la consommation permanente d’oxygène par les cellules. Par un modèle élémentaire EDP, que nous désignons par modèle "Se déplacer ou Se diviser" (Go or Grow en anglais), nous montrons que la combinaisonde la division cellulaire et de l’aérotactisme joue un rôle crucial dans ce comportement collectif. En particulier, cette approche conduit à une formule explicite de la vitesse de propagation.Nous conduisons ensuite une analyse mathématique du modèle "Se déplacer ou Se diviser", qui inclut notamment un résultat d’existence et d’unicité du modèle localement en temps, une analyse de la dynamique intérieure de la population en propagation, ainsi qu’une caractérisation faible du comportement de propagation asymptotique.Suite à ce travail, nous nous interrogeons sur les conditions sous lesquelles une population cellulaire peut se propager, en générant leur propre gradient de signalisation. Nous mentionnons des résultats antérieurs dans la littérature et discutons de divers scénarios de modélisation, qui conduisent à ce type de phénomènes de propagation.Ensuite, nous proposons une approche pour concevoir des schémas numériques bien équilibrés pour des ondes progressives dans des modèles cinétiques et paraboliques. Cette approche combine une estimation de la vitesse de propagation instantanée, ainsi que des techniques documentées dans la littérature pour concevoir des schémas bien équilibrés.Enfin, nous étudions un modèle "Se déplacer ou Se diviser" stochastique et individu-centré, qui se fonde sur une simple règle "Se déplacer ou Se diviser". Nous conjecturons une limite en large population, qui peut être vu comme un modèle "Se déplacer ou Se diviser" alernatif, et étudions numériquement les lignées ancestrales des particules. Ainsi, nous proposons un point de vue parallèle sur les dynamiques intérieures. Le modèle "Sedéplacer ou Se diviser" alternatif est analysée et nous donnons des résultats préliminaires sur le comportement asymptotique de la propagation

Mouvement collectif chez Dictyostelium discoideum et autres espèces. Modélisation, analyse et simulations

This thesis is concerned with the modeling of collective cell movement and the analysis of spreading phenomena arising in these models. The starting point of the thesis is the mathematical modeling of an experiment, where a colony of Dictyostelium discoideum is able to escape hypoxia through a remarkable collective behavior. It is shown that oxygen consumption leads to self-generated oxygen gradients, which serve as directional cues and trigger a collective movement towards higher oxygen regions. This movement is sustained over large scales by the perpetual consumption of oxygen by the cells. Through an elementary PDE model, the so-called Go or Grow model, we show that the combination of cell division and aerotaxis plays a key role in this collective behavior. In particular, this approach leads to an explicit formula for the propagation speed. We carry out a thorough mathematical analysis of the Go or Grow model, including a result of existence and uniqueness locally in time of the model, an analysis of the inside dynamics of the propagating population, as well as a weak characterization of the asymptotic spreading behavior. Following the aforementioned investigation, we address the question under which circumstance a cell population may propagate, by generating their own signaling gradients. We do a survey on existing results in the literature and discuss various modeling scenarios, which lead to this type of propagation phenomena. Then, we propose an approach to design well-balanced numerical schemes for traveling waves in kinetic and parabolic models. The approach combines an estimate of the instantaneous spreading speed with techniques taken from the literature to design well-balanced schemes. Finally, we study a stochastic individual-based Go or Grow model, which is based on a simple Go or Grow rule. We conjecture the large population limit, which can be seen as an alternative Go or Grow model, and investigate numerically the ancestral lineages of particles. This leads to an alternative viewpoint on the inside dynamics. The alternative Go or Grow model is analyzed and we give preliminary results estimating the asymptotic behavior of the spreading.Cette thèse s’inscrit dans le domaine de la modélisation du mouvement cellulaire collectif et de l’analyse de phénomènes de propagation dans ces modèles.Le point de départ de cette thèse est la modélisation mathématique d’une expérience, où une colonie de Dictyostelium discoideum parvient à échapper l’hypoxie grâce à un remarquable comportement collectif. Il est montré que la consommation d’oxygène conduit à des gradients d’oxygène auto-générés, qui servent d’indicateurs de navigation aux cellules et déclenchent un mouvement collectif vers des zones de teneur en oxygène plus élevée. Le mouvement se maintient sur des larges échelles à travers la consommation permanente d’oxygène par les cellules. Par un modèle élémentaire EDP, que nous désignons par modèle "Se déplacer ou Se diviser" (Go or Grow en anglais), nous montrons que la combinaisonde la division cellulaire et de l’aérotactisme joue un rôle crucial dans ce comportement collectif. En particulier, cette approche conduit à une formule explicite de la vitesse de propagation.Nous conduisons ensuite une analyse mathématique du modèle "Se déplacer ou Se diviser", qui inclut notamment un résultat d’existence et d’unicité du modèle localement en temps, une analyse de la dynamique intérieure de la population en propagation, ainsi qu’une caractérisation faible du comportement de propagation asymptotique.Suite à ce travail, nous nous interrogeons sur les conditions sous lesquelles une population cellulaire peut se propager, en générant leur propre gradient de signalisation. Nous mentionnons des résultats antérieurs dans la littérature et discutons de divers scénarios de modélisation, qui conduisent à ce type de phénomènes de propagation.Ensuite, nous proposons une approche pour concevoir des schémas numériques bien équilibrés pour des ondes progressives dans des modèles cinétiques et paraboliques. Cette approche combine une estimation de la vitesse de propagation instantanée, ainsi que des techniques documentées dans la littérature pour concevoir des schémas bien équilibrés.Enfin, nous étudions un modèle "Se déplacer ou Se diviser" stochastique et individu-centré, qui se fonde sur une simple règle "Se déplacer ou Se diviser". Nous conjecturons une limite en large population, qui peut être vu comme un modèle "Se déplacer ou Se diviser" alernatif, et étudions numériquement les lignées ancestrales des particules. Ainsi, nous proposons un point de vue parallèle sur les dynamiques intérieures. Le modèle "Sedéplacer ou Se diviser" alternatif est analysée et nous donnons des résultats préliminaires sur le comportement asymptotique de la propagation

When Self-Generated Gradients interact with Expansion by Cell Division and Diffusion. Analysis of a Minimal Model

We investigate a minimal model for cell propagation involving migration along self-generated signaling gradients and cell division, which has been proposed in an earlier study. The model consists in a system of two coupled parabolic diffusion-advection-reaction equations. Because of a discontinuous advection term, the Cauchy problem should be handled with care. We first establish existence and uniqueness locally in time through the reduction of the problem to the well-posedness of an ODE, under a monotonicity condition on the signaling gradient. Then, we carry out an asymptotic analysis of the system. All positive and bounded traveling waves of the system are computed and an explicit formula for the minimal wave speed is deduced. An analysis on the inside dynamics of the wave establishes a dichotomy between pushed and pulled waves depending on the strength of the advection. We identified the minimal wave speed as the biologically relevant speed, in a weak sense, that is, the solution propagates slower, respectively faster, than the minimal wave speed, up to time extraction. Finally, we extend the study to a hyperbolic two-velocity model with persistence

Kur’an’da el-Cin Kavramının Medlulü Hakkındaki İhtilaflar

Kur’an’da çokanlamlı lafızların medlulünün tespitinde müfessirler arasında çeşitli görüşler ortaya çıkmıştır. Kur’an’da hangi anlama geldiği hususunda ihtilaf edilen çokanlamlı kelimelerden birisi de el-cin lafzıdır. Bu husustaki düşünce farklılığı kelimenin yalın olarak yer aldığı ayetlerde söz konusu olmuştur. Kelimenin eşdizimli kullanımları, bağlamını da açığa vurduğundan herhangi bir anlam ihtilafına mahal bırakmamıştır. Buna karşın yalın hâldeki kullanımlarda muhtelif bağlamsal yaklaşımlara müsait bir zeminin varlığı kelimeye müfessirlerce cinler, melekler, İblis ve şeytanlar gibi muhtelif anlamların yüklenmesine yol açmıştır. Bu konu cinler ve melekler arasında kategorik bir ayrımın yapılıp yapılamayacağı meselesini ve beraberinde meleklerin masum varlıklar olup olmadığı hususundaki kelâmî tartışmayı gündeme getirmiştir. Müfessirlerin çokanlamlı bu kelimeyi ele alırken az çok bağlamsal çizgide hareket ettikleri; siyak-sibak, ayetler arasındaki münasebet, tarihi ve kültürel bağlamla ilgili rivayetler gibi hususları dikkate aldıkları gözlenmektedir. Bu noktada kelimenin etimolojik kökeninin de anlam takdirinde tayin edici unsurlardan biri olduğu müşahede edilmektedir. Bu çalışmada öncelikle Câhiliye Arapları’nın cin ve melek algısından söz edilmiş, ardından klasik sözlüklerden yararlanılarak tefsirlerde bu husustaki yaklaşımların dayandığı dilsel zemine ve rivayetlere değinilmiştir. Konuyla ilgili müfessirlerin ilgili ayetler hakkında muhtelif bağlamsal yaklaşımları esas aldıkları tespit edilmiştir

Birgivi’ nin islam ve Osmanlı hukukundaki yeri ve Feraiz risalesinin edisyon kritiği

ÖZETBir toplumun hukuki yapısı, dini anlayış ve yaşayışı hakkında isabetli yargılarda bulunabilmek için o toplumun bu alanlarda tarihsel süreç içerisindeki deneyimlerinden yararlanmak kaçınılmaz bir durumdur. Bu bakımdan kültürel miras olarak sahip olduğumuz en yakın tarihi tecrübe olan Osmanlılar döneminin ilmi; hukuki ve kültürel alanlarında geniş çaplı araştırmalara ihtiyaç vardır. Bu bakımdan biz sözettiğimiz bilimsel açılıma bir nebzecik de olsa katkıda bulunabiliriz ümidiyle Birgivî'nin İslam ve Osmanlı Hukukundaki Yeri ve Ferâiz Risâlesinin Edisyon Kritiği başlıklı konuyu seçmiş bulunuyoruz. Çalışmamızın "Giriş" bölümünde konuya altyapı olmak üzere, o zamana göre oldukça farklı bir dini tavra sahip olan Birgivî'yi ortaya çıkaran siyasi, sosyal ve ilmi konjonktürü ve bu bağlamdaki tarihi çerçeveyi ortaya koymaya çalıştık.Birinci bölümde Birgivî'yi tanıtıcı mahiyette hayatı, eserleri, ilmi şahsiyeti ve etkileri hakkında özet bilgiler verdik.İkinci bölümde ise "Birgivî'nin İslâm ve Osmanlı Hukukundaki Yeri" başlıklı ana konumuza geçmeden önce İslâm ve Osmanlı Hukukunun mahiyeti, kaynakları ve birbirleriyle ilişkileri hakkında özlü bilgiler vermeye çalıştık. Daha sonra tüm bu bilgilerin bize sağladığı perspektiften yararlanarak Birgivî'nin İslâm ve Osmanlı Hukukundaki yerini tesbit etmeye gayret ettik.Üçüncü bölümü Birgivî'nin "Ferâiz Risâlesi ve Şerhi"ne ayırdık. Burada bu yazma eserin nüshalarının tanıtımını yaptık ve karşılaştırmasını yaptığımız nüshaları sembolleriyle belirttik. Ardından metin tenkidi çalışmasına geçtik.ABSTRACTIt is necessary to study the historical development and experience of a nation in order to understand a nations religious, legal structure. Hence, in order to understand the Current Turkish society it is necessary to study the Ottoman's scientific, culturel and legal experiences, In order to contribuse this process I have chosen the subject of "the place of Birgivî in İslamic an Ottoman law and the eritical eddition of his "Risâlah al-Farâiz"At our study's introduction part, we struggled to bring up the historical frame of political, social and scientific marginality which has come into deing Birgivî who had a different religious attitude in his time. At first pant, we wrote summary knowledges about Birgivî's life, his written works, scientific personality and effects.At second part, before the our main subject. "Birgivî's Place in İslamic an Ottoman Law" we tryed to give pithy knowledges about the reality, spring and contact eachother of İslamic and Ottoman Law.After that we endeavored to establish Birgivî's Place in İslamic and Ottoman Law with these knowledges.We seperated the third part for Feraiz Pamphlet and it's explanation. Here we introduced the editions of that written work and made clear the editions with their symbols. Then we studied the editions criticism

İslam ve Batı / Islam and the West

Abstract The relationships between Islam and the West that has been become high on the agenda for the Islamic world and for our country throughout the last two centuries. It seems that this phenemonen will remain for a long time. Therefore, this topic is one of the major issues that needs to be analyzed extensively because it is mainly concerned with our country’s and Islamic world’s future. The author İbrahim Kalın addressed the historical account of the relationships between Islam and the West quite competently in his book titled “Islam and the West”. The major theme of this work is the way of thinking that there is still a common ground between the two civilisations which have a long history of conflicts, consequently the possibility of creating a peaceful atmosphere between both still exists. We could argue that one of the objectives that the author aimed to accomplish through this book is to provide an intellectual basis for the relations between Islam and the West as well as making a contribution to promoting and developing a dialog and reconcilitation between Muslims and the West. However, it might be an accurate conclusion that the general situation presented or suggestions made by depending on a few good examples in this book rely to a large extent on wishful thinking when we take into consideration that the relations between the two civilisations are based predominantly on prejudice, hostility and aggression along the history. Indeed, the author himself admits this fact in some of the phrases of the book.  Öz İslam dünyasının, özellikle de ülkemizin birkaç asırdır gündemini meşgul eden ve bundan sonra da meşgul edecek gibi görünen İslam-Batı ilişkilerinin doğru ve objektif biçimde derinlemesine ele alınması gerekmektedir. Zira bu konu, İslam dünyasının ve ülkemizin geleceğini çok yakından ilgilendirmektedir. Bu bakımdan, İbrahim Kalın’ın söz konusu eseri büyük önem arz etmektedir. Bu eserin ana temasını, uzun bir tarihi geçmişi olan ve büyük çapta anlaşmazlıklar ve çatışmalar silsilesinden oluşan İslam-Batı ilişkilerinde bazı uzlaşı noktalarının da bulunduğu ve ikisi arasında sağlıklı bir diyalog zemininin oluşturulmasının mümkün olduğu, dolayısıyla bu iki medeniyet arasındaki kavga halinin aslında kaçınılmaz bir durumu yansıtmadığı düşüncesi oluşturmaktadır. Bu temelden hareketle yazar, eserinde İslam ve Batı arasındaki ilişkiler için entelektüel bir zemin oluşturmayı ve iki medeniyet arasında diyalog ve barış ortamının geliştirilmesine katkı sunmayı amaçlamaktadır. İbrahim Kalın’ın birkaç örnekten yola çıkarak iki medeniyet arasında bir uzlaşı zemini oluşturulması yönündeki çabasının, aktüel durum dikkate alındığında, pek gerçekçi görünmediği ve bir temenniden ibaret kalacağı söylenebilir. Aslında yazar da satır aralarında bu gerçeği itiraf etmektedir. Bununla birlikte yazarın tarihsel süreç içinde İslam-Batı ilişkilerini güzel bir üslupla ele aldığı böyle bir çalışma, bir iyi niyet göstergesi olarak son derece değerlidir