Entropy of unimodular Lattice Triangulations

Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achive excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is $C=2.196(3)$ consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.Comment: 6 pages, 7 figure

Human Capital Externalities and the Urban Wage Premium: Two Literatures and their Interrelations

In this paper we survey the recent developments in two empirical literatures at the crossroads of labor and urban economics: Studies about localized human capital externalities (HCE) and about the urban wage premium (UWP). After surveying the methods and main results of each of these two literatures separately, we highlight several interrelations between them. In particular we ask if HCE can be interpreted as one fundamental cause of the UWP, and we discuss if one literature can conceptually learn from the methods that are used by the other one.local labor markets, agglomeration, human capital externalities, urban wage premium

How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erd\"os-R\'enyi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole

Optimierung des Anbaus von Sojabohnen: Bestimmung des Vorfruchtwertes und der N2-Fixierleistung sowie Reduzierung der Bodenbearbeitung

Bisher sind die N2-Fixierung aus der Luft, die N-Salden (N2-Fixierung minus N-Abfuhr) und die Vorfruchtwirkung von Soja für Deutschland nicht beschrieben. Diese wurde in Feldversuchen auf einem konventionell und zwei ökologisch bewirtschafteten Standorten im Vergleich zu Körnererbsen untersucht. Die N2-Fixierung von Soja fiel um knapp 100 (ökologisch) und 40 (konventionell) kg ha-1 höher aus als die der Erbsen. Die N-Bilanz war zwischen Soja und Erbsen vergleichbar. Die Vorfruchtwirkung von Erbsen ist aufgrund eines höheren Ertrages in der Nachfrucht Weizen im ökologischen Landbau höher als die von Soja einzuschätzen. Im konventionellen Anbau unterschied sich dagegen die Leistung des nachfolgenden Weizens nicht. Soja passt auch aufgrund einer hohen Wirtschaftlichkeit sehr gut in die Fruchtfolgen. Im ökologischen Anbau erwirtschaftet sie im Fruchtfolgeausschnitt Körnerleguminose – Weizen einen um etwa ein Drittel höheren Deckungsbeitrag als Erbsen, im konventionellen konnte sie mit der Leistung von Körnermais mithalten. In einem dreijährigen Exaktversuch und in On-Farmversuchen wurde die Eignung von reduzierter Bodenbearbeitung im konventionellen Sojaanbau geprüft. Mit Mulchsaat und Strip-Till konnte Soja agronomisch und ökonomisch erfolgreich angebaut werden. Hingegen war die Direktsaat in gewalzten bzw. abgefahren Grünroggen mit 14,4 dt ha-1 im Ertrag niedriger und hatte einen erheblichen wirtschaftlichen Nachteil. Ferner konnte in Mulchsaat und Strip-Till auf die Applikation von Glyphosat vor der Saat ohne Ertragseinbußen oder einen höheren Unkrautbesatz verzichtet werden

Satisfiability of constraint specifications on XML documents

Jose Meseguer is one of the earliest contributors in the area of Algebraic Specification. In this paper, which we are happy to dedicate to him on the occasion of his 65th birthday, we use ideas and methods coming from that area with the aim of presenting an approach for the specification of the structure of classes of XML documents and for reasoning about them. More precisely, we specify the structure of documents using sets of constraints that are based on XPath and we present inference rules that are shown to define a sound and complete refutation procedure for checking satisfiability of a given specification using tableaux.Peer ReviewedPostprint (author's final draft

The FCC-ee Interaction Region Magnet Design

The design of the region close to the interaction point of the FCC-ee experiments is especially challenging. The beams collide at an angle (+-15 mrad) in the high-field region of the detector solenoid. Moreover, the very low vertical beta_y* of the machine necessitates that the final focusing quadrupoles have a distance from the IP (L*) of around 2 m and therefore are inside the main detector solenoid. The beams should be screened from the effect of the detector magnetic field, and the emittance blow-up due to vertical dispersion in the interaction region should be minimized, while leaving enough space for detector components. Crosstalk between the two final focus quadrupoles, only about 6 cm apart at the tip, should also be minimized.Comment: Poster presented at IPAC16, May 8-13, Busan, Kore

Comparison of Options for the Injector of PS2

In its report, the SPC Review Panel has highlighted that the construction of a 4 MW SPL has to be motivated by the needs of a well-defined and approved physics programme, and that it should be compared with a Rapid Cycling Synchrotron (RCS) when considering only the needs of LHC. This report is meant to answer these remarks by describing the version of the SPL that would be built for the needs of LHC alone (the Low Power SPL or LP-SPL) and by making a preliminary comparison with an RCS

Dynamics of Tipping Cascades on Complex Networks

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change of the system. Many systems with tipping points can be modeled as networks of coupled multistable subsystems, e.g. coupled patches of vegetation, connected lakes, interacting climate tipping elements or multiscale infrastructure systems. In such networks, tipping events in one subsystem are able to induce tipping cascades via domino effects. Here, we investigate the effects of network topology on the occurrence of such cascades. Numerical cascade simulations with a conceptual dynamical model for tipping points are conducted on Erd\H{o}s-R\'enyi, Watts-Strogatz and Barab\'asi-Albert networks. Additionally, we generate more realistic networks using data from moisture-recycling simulations of the Amazon rainforest and compare the results to those obtained for the model networks. We furthermore use a directed configuration model and a stochastic block model which preserve certain topological properties of the Amazon network to understand which of these properties are responsible for its increased vulnerability. We find that clustering and spatial organization increase the vulnerability of networks and can lead to tipping of the whole network. These results could be useful to evaluate which systems are vulnerable or robust due to their network topology and might help to design or manage systems accordingly.Comment: 22 pages, 12 figure