Automatic Palaeographic Exploration of Genizah Manuscripts

The Cairo Genizah is a collection of hand-written documents containing approximately 350,000 fragments of mainly Jewish texts discovered in the late 19th century. The fragments are today spread out in some 75 libraries and private collections worldwide, but there is an ongoing effort to document and catalogue all extant fragments. Palaeographic information plays a key role in the study of the Genizah collection. Script style, and–more specifically–handwriting, can be used to identify fragments that might originate from the same original work. Such matched fragments, commonly referred to as “joins”, are currently identified manually by experts, and presumably only a small fraction of existing joins have been discovered to date. In this work, we show that automatic handwriting matching functions, obtained from non-specific features using a corpus of writing samples, can perform this task quite reliably. In addition, we explore the problem of grouping various Genizah documents by script style, without being provided any prior information about the relevant styles. The automatically obtained grouping agrees, for the most part, with the palaeographic taxonomy. In cases where the method fails, it is due to apparent similarities between related scripts

A Characterization Theorem and An Algorithm for A Convex Hull Problem

Given $S= \{v_1, \dots, v_n\} \subset \mathbb{R} ^m$ and $p \in \mathbb{R} ^m$, testing if $p \in conv(S)$, the convex hull of $S$, is a fundamental problem in computational geometry and linear programming. First, we prove a Euclidean {\it distance duality}, distinct from classical separation theorems such as Farkas Lemma: $p$ lies in $conv(S)$ if and only if for each $p' \in conv(S)$ there exists a {\it pivot}, $v_j \in S$ satisfying $d(p',v_j) \geq d(p,v_j)$. Equivalently, $p \not \in conv(S)$ if and only if there exists a {\it witness}, $p' \in conv(S)$ whose Voronoi cell relative to $p$ contains $S$. A witness separates $p$ from $conv(S)$ and approximate $d(p, conv(S))$ to within a factor of two. Next, we describe the {\it Triangle Algorithm}: given $\epsilon \in (0,1)$, an {\it iterate}, $p' \in conv(S)$, and $v \in S$, if $d(p, p') < \epsilon d(p,v)$, it stops. Otherwise, if there exists a pivot $v_j$, it replace $v$ with $v_j$ and $p'$ with the projection of $p$ onto the line $p'v_j$. Repeating this process, the algorithm terminates in $O(mn \min \{\epsilon^{-2}, c^{-1}\ln \epsilon^{-1} \})$ arithmetic operations, where $c$ is the {\it visibility factor}, a constant satisfying $c \geq \epsilon^2$ and $\sin (\angle pp'v_j) \leq 1/\sqrt{1+c}$, over all iterates $p'$. Additionally, (i) we prove a {\it strict distance duality} and a related minimax theorem, resulting in more effective pivots; (ii) describe $O(mn \ln \epsilon^{-1})$-time algorithms that may compute a witness or a good approximate solution; (iii) prove {\it generalized distance duality} and describe a corresponding generalized Triangle Algorithm; (iv) prove a {\it sensitivity theorem} to analyze the complexity of solving LP feasibility via the Triangle Algorithm. The Triangle Algorithm is practical and competitive with the simplex method, sparse greedy approximation and first-order methods.Comment: 42 pages, 17 figures, 2 tables. This revision only corrects minor typo

Arab wayfinding on land and at sea: An historical comparison of traditional navigation techniques

This thesis investigates the historical significance of traditional Arab navigation technology (after the advent of Islam), drawing upon Arabic primary sources and other relevant literature. Modeling wayfinding as a geographical activity in which members of a culture use its technology to interact spatially with the physical environment, it systematically compares the techniques, tools and other features of Arab wayfinding in two environments, sea and land, forming a transportation network from Mecca in Arabia westward to Spain and eastward to China. It also considers Arab and neighboring cultures as innovators in navigation and geography, including the compilation of maps and text for Al-Idrisi's Book of Roger, which summarized Arab geographical knowledge for the European king, Roger II of Sicily, in 1154 A.D. It concludes by reflecting upon the diffusion and lingering significance of Arab learning in Mediterranean Europe and Africa, suggesting further research to bridge gaps in the historical record

Chemical control of liquid phase separation in the cell

Zellen sind in der Lage, gleichzeitig ganz unterschiedliche biochemische Prozesse zu bewältigen. Dies gelingt ihnen durch eine Einteilung ihres Inneren in Kompartiemente, sogennante Organellen, die die jeweils geeignete biochemische Umgebung für die unterschiedlichen Aufgaben schaffen. Bei membranumschlossenen Kompartimenten ist leicht vorstellbar, dass sie eine andere biochemische Zusammensetzung als ihre Umgebung haben können. Jedoch existieren auch Organelle ohne Membran die durch eine flüssig-flüssig Phasenseparation entstehen. Manche dieser Kompartiemente haben die Fähigkeit, RNA zu binden und Proteinkomplexe auszubilden, während andere auf die Veränderungen innerhalb der Zelle, wie z.B. die Veränderung des pH-Werts und der damit Verbunden Änderung ihres Protonierungszustands, reagieren können. Um diese Prozesse theoretisch analysieren zu können, entwickeln wir zunächst ein allgemeingültiges, thermodynamisches Gerüst, um Systeme zu untersuchen, die im chemischen Gleichgewicht flüssig-flüssig hasensepariert vorliegen können. Dies erlaubt, basierend auf den Erhaltungsgrößen, im chemischen Gleichgewicht thermodynamisch konjungierten Variablen zu identifizieren, welche aus den erhaltenen Komponenten und den zugehörigen chemischen Potentialen bestehen. Mithilfe des obig erwähnten Gerüsts können wir den Einfluss des pH-Wertes auf die flüssig-flüssig Phasenseparation in einem minimalen Modell untersuchen. Dies beschreibt die makromolekulare Phasenseparation, kontrolliert durch Protonierungs- und Deprotonierungreaktionen, welche wiederum vom pH-Wert abhängig sind. Unsere Untersuchung der pH-Abhängigkeit der Phasenseparation kommt zu folgenden Ergebnissen: Erstens liegt die größte Region von Phasenseparation im Phasendiagramm typischerweise im Bereich des isoelektrischen Punkts. Zweitens zeigt das Modell eine Fähigkeit der erneuten Mischung auf. Drittens ist die Topologie des Phasendiagrams von der dominantesten Interaktion bestimmt. Unser Modell stimmt mit experimentellen Beobachtungen zur Phasenseparation von intrinsisch ungeordneten, Proteinen, deren Struktur sich pH abhängig verändern, überein. Das Modell ist außerdem konsistent mit Beobachtungen von Phasenseparation von Proteinen im Zytosol von Hefezellen, die entsteht, wenn der intrazellulare pH-Wert in die Nähe des isoelektrischen Punkt dieser Proteine gebracht wird. Des Weiteren geht diese Arbeit auf den physikalischen Mechanismus ein, mit dem flüssigkeitsähnliche Organellen, sog. P granules, im Organismus Caenorhabditis elegans positioniert werden. Um dieses Phänomen zu analysieren, stellen wir zunächst experimentelle Beobachtungen vor, die zeigen, dass PGL-3, eine Hauptkomponente der P granules, flüssigkeitsähnliche Tropfen bildet, deren Zusammensetzung von RNA moduliert werden kann. Darüber hinaus zeigen wir Daten, die großen Unterschiede zwischen der RNA-Bindungsaffinität von Proteinen wie Mex-5, die für die Positionierung der P granules relevant sind, und solchen, die P granules bilden, wie PGL-3, zeigen. Dies deutet darauf hin, dass eine Konkurrenz zwischen den Bestandteilen der P Granula und MEX-5 um die zur Bindung zur Verfügung stehende RNA besteht, die die Kondensation und Auflösung von P Granula räumlich kontrollieren könnte. Auf diesen experimentellen Befunden aufbauend führen wir ein minimalles Modell ein, in dem wir die Phasenseparation von PGL-3 an Bindungsreaktionen der MEX-5 Proteine und RNA koppeln. Um die experimentellen Beobachtungen beschreiben zu können, muss die Neigung des PGL-3 Proteins zur Phasenseparation zunehmen, wenn es Komplexe mit RNA bildet. Dies unterstützt die Idee, dass MEX-5 diese Phasenseparation unterdrückt, indem es die Anzahl an möglichen RNA-Bindungspartner für PGL-3 herabsetzt und damit die weitere Entstehung derartiger Protein-RNA-Komplexe erschwert. Dieser einfache Mechanismus scheint die Hauptursache dafür zu sein, dass P granules auf der posterioren Seite des Caenorhabditis elegans Embryos zu finden sind.One of the main features of cells is their incredible ability to control biochemical processes in space and time. They do so by organizing their interior in sub-compartments called organelles, each of them with a different biochemical environment that allows them to perform specific tasks in the cell. It is sometimes believed that these compartments need a membrane in order to have a stable biochemical environment and regulat their compositions. However, there are some organelles which lack a membrane and seem to form and organize via liquid-liquid phase separation. Some of the components that form these membraneless organelles have the ability to bind to RNA and form complexes, while some others react to changes in the intracellular environment such as pH variations, which in turn affects their protonation state. In order to study these processes from a theoretical perspective, we develop a generic thermodynamic framework to study systems exhibiting liquid-liquid phase separation at chemical equilibrium. This framework, based on the use of conservation laws in chemical reactions, allow us to identify thermodynamic conjugate variables at chemical equilibrium, which are given by a set of conserved quantities and the corresponding conjugate chemical potentials. Within the aforementioned framework, we introduce a minimal model to study the effect of pH on liquid-liquid phase separation. Our model explains macromolecular phase separation controlled by protonation and deprotonation reactions, which are tuned by the pH of the system. We study the phase behavior of the system as a function of pH. Our main findings are: Firstly, the broadest region of phase separation is typically found at the isoelectric point. Secondly, the system exhibits reentrant behavior. Thirdly, that the dominating interaction in the system determines the topology of the phase diagrams. Our model is in agreement with experimental observations of in vitro protein phase separation of pH-responsive intrinsically disordered proteins, as well as with observations of protein phase separation exhibited by many cytosolic proteins when the intracellular pH in yeast cells is brought close to the isoelectric point of such proteins. Moreover, this work analyses the physical mechanism behind the positioning of liquid-like organelles in the {\it{Caenorhabditis elegans}} organism known as P granules. In order to study this phenomenon, we first present firm experimental evidence showing that PGL-3 protein, a key component of P granules, forms liquid-like drops whose assembly can be modulated by RNA. We then present data showing that the RNA-binding affinity differs significantly between proteins relevant for the positioning of P granules, such as MEX-5 and the proteins forming the P granules, like the aforementioned PGL-3. This points to a possible mechanism of RNA-binding competition between P granule constituents and MEX-5 in order to spatially control the condensation and dissolution of P granules. Based on the experimental evidence, we propose a minimal model in which we couple phase separation of PGL-3 to a set of binding reactions involving the MEX-5 protein and RNA. We find that in order to explain the experimental data, the tendency for phase separation of the PGL-3 protein increases with the formation of complexes of PGL-3 bound to RNA. This therefore supports the idea that MEX-5 inhibits this protein phase separation by depleting the RNA available for PGL-3 to form such complexes. This simple mechanism is at the core of how P granules localize to the posterior side of the Caenorhabditis elegans embryo

Habitat use and movement of proboscis monkeys (Nasalis larvatus) in a degraded and human-modified forest landscape

Proboscis monkeys (Nasalis larvatus) are endemic to Borneo and live in habitats threatened by land clearance for agriculture, aquaculture and timber. This thesis examines the roles of structural and landscape characteristics on both short- and long-term habitat use through the first application of GPS tags to proboscis monkeys. In a comparison of four home range estimators, biased random bridges provided the best home range estimates given the GPS-collar dataset and landscape characteristics (Chapter 3). Differences in long-term ranging patterns of 10 individuals across a range of forest-block sizes and disturbance levels were examined, as well as daily and seasonal variation in movement and sleeping site selection. Using Light Detection and Ranging (LiDAR) structural metrics of the forest, as well as landscape characteristics, forest with taller canopies, forests in close proximity to river edges were found to be of particular importance to proboscis monkeys, and plantation edges were avoided (Chapter 4). Changes in daily and monthly movements were associated with seasonal changes in rainfall and potential food availability. Movement patterns also changed near forest edges, with faster, more direct movements near agricultural boundaries. Less rainfall, higher temperatures and brighter moon phases correlated with selection of sleeping sites in the forest interior (Chapter 5). By understanding the ranging requirements of proboscis monkeys, drone and GPS collar data were combined to inform conservation policy (Chapter 6). This thesis provides the most in-depth examination of proboscis monkey ecology to date. They appeared more generalist in their home range use and structural habitat requirements than previously realised, suggesting a higher degree of versatility and resilience to habitat loss and degradation. This study provides increased understanding of potential consequences of human-mediated disturbances and can be used to assist in the protection of this charismatic species and the management of degraded landscapes