A New Athenian Gymnasium from the 4th Century BC?

Schriftquellen belegen, dass das Gymnasium der Athener Akademie vom 6. Jh. v. Chr. bis mindestens zum 2. Jh. n. Chr. benutzt wurde. Der Ort wurde anhand von Texten und einem Horosstein lokalisiert und seit 1929 mehrfach untersucht. Zu den freigelegten Strukturen gehören im Süden ein recht­eckiger Bau mit Hof, der als Palaestra der Akademie gedeutet wurde, und im Norden ein großer quadratischer Peristylbau, der wenig beachtet wurde. Dieser Beitrag revidiert die Identifizierung der beiden Bauten. Es wird gezeigt, dass der Hof des südlichen Baus in die Spätantike gehört und nicht als Palaestra fungiert haben kann. Stattdessen ist der quadratische Bau, dessen Peristyl von Räumen umgeben und der ins 4. Jh. v. Chr. zu datieren ist, anhand von Plan und Inschriften als Palaestra zu identifizieren

The Horrocks-Mumford bundle restricted to planes

We study the behavior of the Horrocks-Mumford bundle when restricted to a plane P^2 in P^4, looking for all possible minimal free resolutions for the restricted bundle. To each of the 6 resolutions (4 stable and 2 unstable) we find, we then associate a subvariety of the Grassmannian G(2,4) of planes in P^4. We thus obtain a filtration of the Grassmannian, which we describe in the second part of this work.Comment: 19 pages, typos removed, added details in Propostions 2.1 and 3.

Organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids

In this work, we present an organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids using arylidene azlactones as starting materials. The developed two step synthesis involves a sequential catalysis approach, in which two different catalysts act sequentially to control the absolute configuration of two different stereocenters. With an accurate selection of the catalysts absolute configuration it is possible to obtain all the stereoisomers of the product. The first synthetic step is a catalytic asymmetric transfer hydrogenation of the azlactone C=C double bond. A Jacobsen type thiourea and a Hantzsch ester were chosen as chiral catalyst and hydride donor, respectively. Different azlactones, Hantzsch esters and thioureas were synthetized and tested in the asymmetric transfer hydrogenation to achieve the best stereoselectivity. The second step involves a dynamic kinetic resolution on the reduced azlactone, through a nucleophilic addition to the carbonyl moiety promoted by a bifunctional chiral catalyst. A wide range of nucleophiles and organocatalysts were tested; the best results were reached with alcohols as nucleophiles and squaramide-based cinchona alkaloids as a chiral catalysts. With the optimized conditions two stereodivergent syntheses were then performed, enabling the selective obtainment of both diastereoisomeric product with high enantioselectivities

Higher order corrections to the effective potential close to the jamming transition in the perceptron model

We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.Comment: 14 pages, 4 figure

The Interlace Polynomial

In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.Comment: 18 pages, 5 figures, to appear as a chapter in: Graph Polynomials, edited by M. Dehmer et al., CRC Press/Taylor & Francis Group, LL