Global and local players in a model of spatial competition

We consider Hotelling location games with global and local players. Global players are active in several markets, while local players act in a single market only. The decisive feature is that global players cannot tailor their product to each market but have to choose a location on the Hotelling line that is valid for all markets in which they are active. Obvious examples include the media industry and politics, where competitors typically compete in several markets with basically the same product. We determine equilibrium configurations for simple specifications of such games. We then show that the presence of gp s tends to induce lower product diversity across markets. Finally, when the number of firms is endogenous, we show how gp s may use their location choice as a preemptive deviceHotelling location games; spatial competition; multiple markets; product differentiation; diversity; preemption

Dynamic Location Games

We study a location game where consumers are distributed according to some density f and where market entry is costly and occurs sequentially. This permits an endogenous determination of the number of active ¯rms, their locations and the sequence in which these locations are occupied. While in general the analysis of such games is complicated by the fact that equilibrium locations and the sequence of settlement must be determined simul-taneously, we show that they can be independently derived for certain classes of densities including monotone and, under some additional restrictions, hump-shaped and U-shaped ones. For these classes we characterize the subgame perfect equilibrium outcome. More-over, when f is monotone and concave the equilibrium locations in areas where the density is larger tend to be more pro¯table. When f is uniform the number of ¯rms entering in equilibrium is minimal.Spatial competition product differentiation dynamic games entry deterrence

Structural similarity between dry and wet sphere packings

The mechanical properties of granular materials change significantly in the presence of a wetting liquid which creates capillary bridges between the particles. Here we demonstrate, using X-ray tomographies of dry and wet sphere packings, that this change in mechanical properties is not accompanied by structural differences between the packings. We characterize the latter by the average numbers of contacts of each sphere $\langle Z\rangle$ and the shape isotropy $\langle \beta_0^{2,0} \rangle$ of the Voronoi cells of the particles. Additionally, we show that the number of liquid bridges per sphere $\langle B\rangle$ is approximately equal to $\langle Z\rangle + 2$, independent of the volume fraction of the packing. These findings will be helpful in guiding the development of both particle-based models and continuum mechanical descriptions of wet granular matter.Comment: slightly revised versio

Efficient coupling to an optical resonator by exploiting time-reversal symmetry

The interaction of a cavity with an external field is symmetric under time reversal. Thus, coupling to a resonator is most efficient when the incident light is the time reversed version of a free cavity decay, i.e. when it has a rising exponential shape matching the cavity lifetime. For light entering the cavity from only one side, the maximally achievable coupling efficiency is limited by the choice of the cavity mirrors' reflectivities. Such an empty-cavity experiment serves also as a model system for single-photon single-atom absorption dynamics. We present experiments coupling exponentially rising pulses to a cavity system which allows for high coupling efficiencies. The influence of the time constant of the rising exponential is investigated as well as the effect of a finite pulse duration. We demonstrate coupling 94% of the incident TEM00 mode into the resonator.Comment: 7 pages, 5 figure

Machine learning for the history of ideas

The information technological progress that has been achieved over the last decades has also given the humanities the opportunity to expand their methodological toolbox. This paper explores how recent advancements in natural language processing may be used for research in the history of ideas so as to overcome traditional scholarship's inevitably selective approach to historical sources. By employing two machine learning techniques whose potential for the analysis of conceptual continuities and innovations has never been considered before, we aim to determine the extent to which they can enhance conventional research methods. It will amount to a critical evaluation of how the advantages of computational in-breadth analysis could be combined with the merits of traditional in-depth analysis in a philosophically fruitful way. After a brief technical description, the approach will be applied to an example: the conceptual (dis)continuity between medieval and early modern philosophy. All the challenges encountered during development and application will be carefully evaluated. We will then be able to assess whether these tools and techniques present promising extensions to the methodological toolbox of traditional scholarship, or whether they do not yet have the potential for a task as complex as the analysis of philosophical literature. The present investigation can thus be seen as an experiment on how far one can go with current machine-learning techniques in this area of research. In doing so, it provides important insights and guidance for future advances in the field.Peer Reviewe

Electron Counting Rules and Electronic Structure in Tetrameric Transition-Metal (T)-Centered Rare-Earth (R) Cluster Complex Halides (X)

Electron partition schemes are a beneficial means to systematize bonding networks and to identify structure-bonding relationships in polar intermetallics. One prolific class of polymetal networks with simple counterions is the broad family of transition-metal (T)-centered rare-earth metal (R) cluster halides (X), which can be isolated or condensed to oligomers and chains. While the electronic structures of R cluster monomers and chains encapsulating T atoms have been studied systematically, the band structures of oligomers, in particular, the most frequent Friauf-type {T4R16} tetramers, have been investigated to a lesser extent. Therefore, the band structures of prototypical compounds with {T4R16}-type tetramers, while maintaining different compositions, were analyzed employing density functional theory based methods. Furthermore, these theoretical examinations provide insight into the origin of the 15 electron rule, which is significant for this class of compounds and correlates with the closed-shell configurations for these structures. Additional research focused on the band structure of monoclinic {Ru4Gd16}Br23, which is composed of rhomboid-shaped {Ru4Gd16} tetramers

Pomelo, a tool for computing Generic Set Voronoi Diagrams of Aspherical Particles of Arbitrary Shape

We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pearsComment: 4 pages, 9 figures, Submitted to Powders and Grains 201

Episodic memory retrieval functionally relies on very rapid reactivation of sensory information

Episodic memory retrieval is assumed to rely on the rapid reactivation of sensory information that was present during encoding, a process termed “ecphory.” We investigated the functional relevance of this scarcely understood process in two experiments in human participants. We presented stimuli to the left or right of fixation at encoding, followed by an episodic memory test with centrally presented retrieval cues. This allowed us to track the reactivation of lateralized sensory memory traces during retrieval. Successful episodic retrieval led to a very early (∼100–200 ms) reactivation of lateralized alpha/beta (10–25 Hz) electroencephalographic (EEG) power decreases in the visual cortex contralateral to the visual field at encoding. Applying rhythmic transcranial magnetic stimulation to interfere with early retrieval processing in the visual cortex led to decreased episodic memory performance specifically for items encoded in the visual field contralateral to the site of stimulation. These results demonstrate, for the first time, that episodic memory functionally relies on very rapid reactivation of sensory information