Reviel Netz

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.