The Average-Case Area of Heilbronn-Type Triangles

From among ${n \choose 3}$ triangles with vertices chosen from $n$ points in the unit square, let $T$ be the one with the smallest area, and let $A$ be the area of $T$. Heilbronn's triangle problem asks for the maximum value assumed by $A$ over all choices of $n$ points. We consider the average-case: If the $n$ points are chosen independently and at random (with a uniform distribution), then there exist positive constants $c$ and $C$ such that $c/n^3 < \mu_n < C/n^3$ for all large enough values of $n$, where $\mu_n$ is the expectation of $A$. Moreover, $c/n^3 < A < C/n^3$, with probability close to one. Our proof uses the incompressibility method based on Kolmogorov complexity; it actually determines the area of the smallest triangle for an arrangement in ``general position.''Comment: 13 pages, LaTeX, 1 figure,Popular treatment in D. Mackenzie, On a roll, {\em New Scientist}, November 6, 1999, 44--4

Knowledge and Civil Society

This open access book focuses on the role of civil society in the creation, dissemination, and interpretation of knowledge in geographical contexts. It offers original, interdisciplinary and counterintuitive perspectives on civil society. The book includes reflections on civil and uncivil society, the role of civil society as a change agent, and on civil society perspectives of undone science. Conceptual approaches go beyond the tripartite division of public, private and civic sectors to propose new frameworks of civic networks and philanthropic fields, which take an inclusive view of the connectivity of civic agency across sectors. This includes relational analyses of epistemic power in civic knowledge networks as well as of regional giving and philanthropy. The original empirical case studies examine traditional forms of civic engagement, such as the German landwomen’s associations, as well as novel types of organizations, such as giving circles and time banks in their geographical context. The book also offers insider reflections on doing civil society, such as the cases of the Umbrella Movement in Hong Kong, epistemic activism in the United States, and the #FeesMustFall movement in South Africa

Knowledge and Civil Society

This open access book focuses on the role of civil society in the creation, dissemination, and interpretation of knowledge in geographical contexts. It offers original, interdisciplinary and counterintuitive perspectives on civil society. The book includes reflections on civil and uncivil society, the role of civil society as a change agent, and on civil society perspectives of undone science. Conceptual approaches go beyond the tripartite division of public, private and civic sectors to propose new frameworks of civic networks and philanthropic fields, which take an inclusive view of the connectivity of civic agency across sectors. This includes relational analyses of epistemic power in civic knowledge networks as well as of regional giving and philanthropy. The original empirical case studies examine traditional forms of civic engagement, such as the German landwomen’s associations, as well as novel types of organizations, such as giving circles and time banks in their geographical context. The book also offers insider reflections on doing civil society, such as the cases of the Umbrella Movement in Hong Kong, epistemic activism in the United States, and the #FeesMustFall movement in South Africa

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Archery by the Apaches – implications of using the bow and arrow in hunter-gatherer communities

This review focuses on the technical and social details of production, training, and use of archery equipment by a Native American tribe, the Apaches. The study aims to understand the use of the bow in the Mesolithic and Early and Middle Neolithic societies of the Old World. The paper further describes arrow ballistics. An arrow and bow with similar dimensions and materials to those used by the Apaches was reconstructed and used in ballistic experiments. Shooting and the subsequent model calculation showed that the effective range of arrows made of reed and projected by a bow of medium strength (16–18kg) was not more than approx. 20m. Due to the initial flat part of the ballistic trajectory, such arrows were quite efficient in close-range contests. Within the model calculation, a regression procedure was introduced to determine the arrow air-drag parameters from an ensemble of shots.Članek podaja pregled o tehničnih in socioloških podrobnostih pri izdelavi, treningu in rabi lokostrelske opreme pri ameriškem domorodnem plemenu Apačev. Študija je namenjena razumevanju rabe loka in puščic v mezolitskih ter zgodnje in srednje neolitskih kulturah Starega sveta. Drugi del študije se ukvarja z balistiko puščice. Predmet balističnih preizkusov sta bila puščica in lok podobnih dimenzij in materialov, kot so jih uporabljali Apači. Streljanje in modelsko računanje sta pokazala, da uporabni doseg puščice, izdelane iz trstike in izstreljene z loka srednje moči (16–18 kg), ni večji od približno 20 metrov. Ker je balistična krivulja take puščice v prvem delu leta zelo položna, so bile puščice izredno učinkovite na kratko razdaljo. V modelskem računu smo uvedli nov postopek za določanje parametrov zračnega upora iz skupine strelov

Lateral Organization and Thermodynamics of Coiled-coil Lipopeptides - Implications for Docking and Fusion Efficiency

Specific cellular membrane interaction is a crucial point in nature as it facilitates key processes like cell-cell communication or membrane fusion. The latter one is highly controlled frequently mediated by the superfamily of SNARE proteins (soluble N-ethylmaleimide-sensitive factor attachment protein receptor) in eukaryotic cells. The definite mechanism behind this process is still poorly understood, but the coiled-coil formation of the SNARE core complex consisting of four α-helices seems to generate the fusogenic driving force. This offers the possibility to design a straightforward experimental setup to mimic the complex protein-mediated membrane-membrane interaction by using mere protein fragments or peptides attached to artificial lipid bilayers, which self-assemble into a coiled-coil structure. In this work, three different sets of artificial coiled-coil forming peptides were synthesized and subsequently attached to maleimide containing phospholipids in membranes via an in situ coupling reaction generating a highly controllable functionalization protocol. Thus, secondary structure changes, kinetics as well as thermodynamic characteristics were monitored during coiled-coil formation in solution and on solid supported membranes with e.g. time-resolved ellipsometry, IR and CD spectroscopy. A distinct loss of entropy upon heterodimerization of peptides on surfaces was found. This could be correlated with a self-assembled lateral clustering of lipopeptides in membranes leading to translational immobilization of hybrid structures. Strikingly, these dense and highly ordered clusters, which act as obstacles for surrounding matrix lipids, undergo a slow but detectable reorganization process causing a partial dissolution of the found clusters upon coiled-coil formation. Furthermore, an increasing fusogenicity was shown, which was correlated to the degree of cluster formation. Upon focusing on energetic and as well structural characteristics, the established model system gives the possibility to screen the docking and fusion ability of different coiled-coil forming peptides leading to an ideal mimic for SNARE mediated membrane fusion

The Seven Sleepers And The Seven Kneelers: Prolegomena To A Study Of The Belles Verrières Of The Cathedral Of Rouen

The recomposed, much-altered, and partially dispersed vestiges of the original nave-aisle glazing of Rouen Cathedral--the so-called Belles Verrières --constitute one of the most important but least studied ensembles of early 13th-century French stained glass. This article will address two windows represented in the Belles Verrières as a means of exploring a working methodology for reconstructing the Rouen nave-aisle glazing. From a close analysis of all remaining fragments, the original design of the Seven Sleepers of Ephesus and John the Evangelist windows will be reconstructed. Once assembled, each window will be evaluated in relation to stylistic, iconographic and historical contexts. The iconography of the Seven Sleepers, closely tied to the political history of Normandy at the turn of the 13th century, will allow that window to be dated with rare precision to the years between 1200-1202. The stylistic relationship between the John the Evangelist window and other glass at Rouen and Beauvais will argue for a date significantly later, in the 1240s. It thus appears that the glazing of the nave aisle at Rouen extended throughout the first half of the 13th century, rather than being restricted to the first two decades, as is usually assumed