Predicting the binding mode of flexible polypeptides to proteins is an important task that falls outside the domain of applicability of most small molecule and protein-protein docking tools. Here, we test the small molecule flexible ligand docking program Glide on a set of 19 non-α-helical peptides and systematically improve pose prediction accuracy by enhancing Glide sampling for flexible polypeptides. In addition, scoring of the poses was improved by post-processing with physics-based implicit solvent MM- GBSA calculations. Using the best RMSD among (...) the top 10 scoring poses as a metric, the success rate (RMSD ≤ 2.0 \textbackslash AA for the interface backbone atoms) increased from 21 with default Glide SP settings to 58 with the enhanced peptide sampling and scoring protocol in the case of redocking to the native protein structure. This approaches the accuracy of the recently developed Rosetta FlexPepDock method (63 success for these 19 peptides) while being over 100 times faster. Cross-docking was performed for a subset of cases where an unbound receptor structure was available, and in that case, 40 of peptides were docked successfully. We analyze the results and find that the optimized polypeptide protocol is most accurate for extended peptides of limited size and number of formal charges, defining a domain of applicability for this approach. (shrink)

Gibt es Elemente, Bestandteile, Strukturen, die in allen Wissenschaftsbereichen, Disziplinen und Theorien fast gleich sind? Dieses Buch stellt ein neues und originelles Modell für Theorien, Theoriennetze und dynamische Entwicklungen vor, das für empirische Untersuchungen in den Sozialwissenschaften, für Computersimulationen, aber auch für praktisch-politische Anwendungen geeignet ist. Die Grundelemente in diesem Modell sind Ereignisse, Fakten, Modelle, Netze und Wahrscheinlichkeit.

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

In this chapter, I review the argument of “The Shaping of Deduction in Greek Mathematics,” explaining its elements that may be construed as “semiological,” comparing them with other work I did in the semiology of mathematics, and conclude by pointing out the scope, and limits, of semiological explanation in the history of mathematics.

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

This book offers a critical introduction to the work of American philosopher D. G. Leahy (1937-2014). Leahy's fundamental thinking can be characterized as an absolute creativity in which all creating is 'live' -- a happening occurring now that manifests a supersaturated polyontological actuality that is essentially created by the logic that characterizes it. Leahy leaves behind the categorial presuppositions of modern thought, eclipsing both Cartesian and Hegelian subjectivities and introducing instead an essentially new form of thinking founded in a nondual (...) logic of creation. The new thinking delineates the absolute unicity of existence as a creative interactivity beyond all traditional dichotomies (such as one vs. many, unity vs. plurality, identity vs. change): a fully "digitized" actuality that is nothing but newness, which inherently implies nothing but change. Through this new form of thinking, change itself is revealed to be the very essence of reality and mind. Any reader looking for a quantum leap beyond the thrall of modern and postmodern fixations is invited to hear and apprehend this new thinking that refuses to be conditioned by paradigms, categories, species, genera, walls, bridges, boundaries, or abstractions: an essentially free thinking that embodies creative novelty itself. (shrink)

The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the (...) localized solution we see a transition to a practice of mathematics based on the systematic approach. With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics. (shrink)

This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor (...) class='Hi'>Netz argues that Hellenistic mathematical writings adopt a narrative strategy based on surprise, a compositional form based on a mosaic of apparently unrelated elements, and a carnivalesque profusion of detail. He further investigates how such stylistic preferences derive from, and throw light on, the style of Hellenistic poetry. This important book will be welcomed by all scholars of Hellenistic civilization as well as historians of ancient science and Western mathematics. (shrink)

Based on the evidence of the likely near-contemporary mathematical practice of diagrams, this article proposes a possible reconstruction of Aristotle’s three figures as introduced in Prior Analytics 1.4–6.

Greek culture matters because its unique pluralistic debate shaped modern discourses. This ground-breaking book explains this feature by retelling the history of ancient literary culture through the lenses of canon, space and scale. It proceeds from the invention of the performative 'author' in the archaic symposium through the 'polis of letters' enabled by Athenian democracy and into the Hellenistic era, where one's space mattered and culture became bifurcated between Athens and Alexandria. This duality was reconfigured into an eclectic variety consumed (...) by Roman patrons and predicated on scale, with about a thousand authors active at any given moment. As patronage dried up in the third century CE, scale collapsed and literary culture was reduced to the teaching of a narrower field of authors, paving the way for the Middle Ages. The result is a new history of ancient culture which is sociological, quantitative, and all-encompassing, cutting through eras and genres. (shrink)

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that such (...) operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction. (shrink)

There are a number of ways in which Greek mathematics can be seen to be radically original. First, at the level of mathematical contents: many objects and results were first discovered by Greek mathematicians. Second, Greek mathematics was original at the level of logical form: it is arguable that no form of mathematics was ever axiomatic independently of the influence of Greek mathematics. Finally, third, Greek mathematics was original at the level of form, of presentation: Greek mathematics is written in (...) its own specific, original style. This style may vary from author to author, as well as within the works of a single author, but it is still always recognizable as the Greek mathematical style. This style is characterized by the use of the lettered diagram, a specific technical terminology, and a system of short phrases. I believe this third aspect of the originality—the style—was responsible, indirectly, for the two other aspects of the originality. The style was a tool, with which Greek mathematicians were able to produce results of a given kind, and to produce them in a special, compelling way. This tool, I claim, emerged organically, and reflected the communication-situation in which Greek mathematics was conducted. For all this I have argued elsewhere. (shrink)

This article makes two claims. The first is that Archimedes’ On Floating Bodies included a punning reference, in its key diagrammatic figure AΠΟΛ: the precise purpose of the pun may not be recovered by us, but even so it remains a powerful example of the playful in Archimedes’ writing. The second is that Apollonius could have been Archimedes’ younger contemporary. The outcome could be that we find Archimedes addressing a playful, hidden message to Apollonius, providing us with a unique insight (...) into the communication of Greek mathematics. (shrink)

Reviews in Common Knowledge generally seek to be more cool and edgy than their subjects, an impossibility in this case. Ording takes a mathematical statement and reaches it in ninety-nine different ways. This book is quite literally a page-turner: most of the arguments take the recto page, with comments on their verso. One keeps cycling back and forth between the mathematical inventiveness of the recto and the philosophical elegance of the verso. The ambition is huge—to construct a mathematical counterpart to (...) Queneau's masterpiece Exercises de Style—and, remarkably, this ambition is fulfilled.It is interesting that Queneau's variations are much closer to each other than Ording's are. Queneau often feels free to provide, as a variation, the very same text with a fundamentally grammatical transformation (switching the order of the descriptions, changing their tenses, and so forth). Most of the time, Ording feels obliged to come up with a significantly different argument. Indeed, his fixed core is less constraining: instead of following the same narrative arc in different forms, he merely has to reach the same endpoint. Ording's book is rather like ninety-nine different jokes leading to the same punch line. To be clear: it is perfectly possible to produce the precise same narrative arc, in mathematics, via different forms. Switching the order is a normal way in which such exercises in mathematical style are actually produced (mathematicians do have to decide whether to write “P, therefore Q” or to write “Q, since P”). Evidently, Ording felt that producing many such purely grammatical and formal transformations would feel tedious, which is fair enough but is not precisely a contrast between mathematics and literature. Queneau's variations are, indeed, tedious; delightfully tedious; delightful in their tediousness. Joyce as a tasting menu. Some readers of modernist literature can take delight in a certain tediousness, but Ording has no illusions concerning the audience for mathematics, and, to make his own variations appealing, he had to make them much more interesting than Queneau's. The result is brilliant and should be read by anyone interested in mathematics, literature, and their many parallels and variations. (shrink)

The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in (...) the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created. (shrink)

Archimedes was the greatest scientist of antiquity and one of the greatest of all time. This book is Volume I of the first authoritative translation of his works into English. It is also the first publication of a major ancient Greek mathematician to include a critical edition of the diagrams and the first translation into English of Eutocius' ancient commentary on Archimedes. Furthermore, it is the first work to offer recent evidence based on the Archimedes Palimpsest, the major source for (...) Archimedes, lost between 1915 and 1998. A commentary on the translated text studies the cognitive practice assumed in writing and reading the work, and it is Reviel Netz's aim to recover the original function of the text as an act of communication. Particular attention is paid to the aesthetic dimension of Archimedes' writings. Taken as a whole, the commentary offers a groundbreaking approach to the study of mathematical texts. (shrink)

ZusammenfassungDer Artikel stellt die Methodik zur Erforschung einer „Bibliosphäre“ vor, also der Gesamtheit der literarischen Dokumente einer bestimmten Kultur. In diesem Fall geht es um die Bibliosphäre der Antike, und hierbei insbesondere um deren wissenschaftlich-philosophischen Bereich. Es wird die Auffassung vertreten, dass wir die Inhalte von Werken durch ihre Position in der Bibliosphäre begreifen können. Der Gegensatz zwischen Mathematik und Literatur wird detailliert dargestellt und der Übergangscharakter der Medizin hervorgehoben.

ZusammenfassungDer Artikel stellt die Methodik zur Erforschung einer „Bibliosphäre“ vor, also der Gesamtheit der literarischen Dokumente einer bestimmten Kultur. In diesem Fall geht es um die Bibliosphäre der Antike, und hierbei insbesondere um deren wissenschaftlich-philosophischen Bereich. Es wird die Auffassung vertreten, dass wir die Inhalte von Werken durch ihre Position in der Bibliosphäre begreifen können. Der Gegensatz zwischen Mathematik und Literatur wird detailliert dargestellt und der Übergangscharakter der Medizin hervorgehoben.

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (shrink)

In this first paperback edition, a new introduction by Tom Burke establishes the ongoing importance of Sleeper's analysis of the integrity of Dewey's work and ...

Political liberals ask citizens not to appeal to certain considerations, including religious and philosophical convictions, in political deliberation. We argue that political liberals must include a demanding requirement of intellectual modesty in their ideal of citizenship in order to motivate this deliberative restraint. The requirement calls on each citizen to believe that the best reasoners disagree about the considerations that she is barred from appealing to. Along the way, we clarify how requirements of intellectual modesty relate to moral reasons for (...) deliberative restraint. And we argue against attempts to weaken our requirement of intellectual modesty by emphasizing those moral reasons. (shrink)