TY - JOUR A1 - Schlosser, Rainer T1 - Stochastic dynamic pricing and advertising in isoelastic oligopoly models JF - European Journal of Operational Research N2 - In this paper, we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity. We consider the sale of perishable as well as durable goods and include adoption effects in the demand. Based on a unique stochastic feedback Nash equilibrium, we derive closed-form solution formulas of the value functions and the optimal feedback policies of all competing firms. Efficient simulation techniques are used to evaluate optimally controlled sales processes over time. This way, the evolution of optimal controls as well as the firms’ profit distributions are analyzed. Moreover, we are able to compare feedback solutions of the stochastic model with its deterministic counterpart. We show that the market power of the competing firms is exactly the same as in the deterministic version of the model. Further, we discover two fundamental effects that determine the relation between both models. First, the volatility in demand results in a decline of expected profits compared to the deterministic model. Second, we find that saturation effects in demand have an opposite character. We show that the second effect can be strong enough to either exactly balance or even overcompensate the first one. As a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model. KW - Pricing KW - Advertising KW - Stochastic differential games KW - Oligopoly competition KW - Adoption effects Y1 - 2017 U6 - https://doi.org/10.1016/j.ejor.2016.11.021 SN - 0377-2217 SN - 1872-6860 VL - 259 SP - 1144 EP - 1155 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Buschmann, Stefan A1 - Trapp, Matthias A1 - Döllner, Jürgen Roland Friedrich T1 - Animated visualization of spatial-temporal trajectory data for air-traffic analysis JF - The Visual Computer N2 - With increasing numbers of flights worldwide and a continuing rise in airport traffic, air-traffic management is faced with a number of challenges. These include monitoring, reporting, planning, and problem analysis of past and current air traffic, e.g., to identify hotspots, minimize delays, or to optimize sector assignments to air-traffic controllers. To cope with these challenges, cyber worlds can be used for interactive visual analysis and analytical reasoning based on aircraft trajectory data. However, with growing data size and complexity, visualization requires high computational efficiency to process that data within real-time constraints. This paper presents a technique for real-time animated visualization of massive trajectory data. It enables (1) interactive spatio-temporal filtering, (2) generic mapping of trajectory attributes to geometric representations and appearance, and (3) real-time rendering within 3D virtual environments such as virtual 3D airport or 3D city models. Different visualization metaphors can be efficiently built upon this technique such as temporal focus+context, density maps, or overview+detail methods. As a general-purpose visualization technique, it can be applied to general 3D and 3+1D trajectory data, e.g., traffic movement data, geo-referenced networks, or spatio-temporal data, and it supports related visual analytics and data mining tasks within cyber worlds. KW - Spatio-temporal visualization KW - Trajectory visualization KW - 3D visualization KW - Visual analytics KW - Real-time rendering Y1 - 2016 U6 - https://doi.org/10.1007/s00371-015-1185-9 SN - 0178-2789 SN - 1432-2315 VL - 32 SP - 371 EP - 381 PB - Springer CY - New York ER - TY - CHAP ED - Meinel, Christoph ED - Polze, Andreas ED - Oswald, Gerhard ED - Strotmann, Rolf ED - Seibold, Ulrich ED - Schulzki, Bernhard T1 - HPI Future SOC Lab BT - Proceedings 2016 N2 - The “HPI Future SOC Lab” is a cooperation of the Hasso Plattner Institute (HPI) and industrial partners. Its mission is to enable and promote exchange and interaction between the research community and the industrial partners. The HPI Future SOC Lab provides researchers with free of charge access to a complete infrastructure of state of the art hard and software. This infrastructure includes components, which might be too expensive for an ordinary research environment, such as servers with up to 64 cores and 2 TB main memory. The offerings address researchers particularly from but not limited to the areas of computer science and business information systems. Main areas of research include cloud computing, parallelization, and In-Memory technologies. This technical report presents results of research projects executed in 2016. Selected projects have presented their results on April 5th and November 3th 2016 at the Future SOC Lab Day events. N2 - Das Future SOC Lab am HPI ist eine Kooperation des Hasso-Plattner-Instituts mit verschiedenen Industriepartnern. Seine Aufgabe ist die Ermöglichung und Förderung des Austausches zwischen Forschungsgemeinschaft und Industrie. Am Lab wird interessierten Wissenschaftlern eine Infrastruktur von neuester Hard- und Software kostenfrei für Forschungszwecke zur Verfügung gestellt. Dazu zählen teilweise noch nicht am Markt verfügbare Technologien, die im normalen Hochschulbereich in der Regel nicht zu finanzieren wären, bspw. Server mit bis zu 64 Cores und 2 TB Hauptspeicher. Diese Angebote richten sich insbesondere an Wissenschaftler in den Gebieten Informatik und Wirtschaftsinformatik. Einige der Schwerpunkte sind Cloud Computing, Parallelisierung und In-Memory Technologien. In diesem Technischen Bericht werden die Ergebnisse der Forschungsprojekte des Jahres 2016 vorgestellt. Ausgewählte Projekte stellten ihre Ergebnisse am 5. April 2016 und 3. November 2016 im Rahmen der Future SOC Lab Tag Veranstaltungen vor. KW - Future SOC Lab KW - research projects KW - multicore architectures KW - In-Memory technology KW - cloud computing KW - machine learning KW - artifical intelligence KW - Future SOC Lab KW - Forschungsprojekte KW - Multicore Architekturen KW - In-Memory Technologie KW - Cloud Computing KW - maschinelles Lernen KW - künstliche Intelligenz Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-406787 ER - TY - THES A1 - Krohmer, Anton T1 - Structures & algorithms in hyperbolic random graphs T1 - Strukturen & Algorithmen in Hyperbolischen Zufallsgraphen N2 - Complex networks are ubiquitous in nature and society. They appear in vastly different domains, for instance as social networks, biological interactions or communication networks. Yet in spite of their different origins, these networks share many structural characteristics. For instance, their degree distribution typically follows a power law. This means that the fraction of vertices of degree k is proportional to k^(−β) for some constant β; making these networks highly inhomogeneous. Furthermore, they also typically have high clustering, meaning that links between two nodes are more likely to appear if they have a neighbor in common. To mathematically study the behavior of such networks, they are often modeled as random graphs. Many of the popular models like inhomogeneous random graphs or Preferential Attachment excel at producing a power law degree distribution. Clustering, on the other hand, is in these models either not present or artificially enforced. Hyperbolic random graphs bridge this gap by assuming an underlying geometry to the graph: Each vertex is assigned coordinates in the hyperbolic plane, and two vertices are connected if they are nearby. Clustering then emerges as a natural consequence: Two nodes joined by an edge are close by and therefore have many neighbors in common. On the other hand, the exponential expansion of space in the hyperbolic plane naturally produces a power law degree sequence. Due to the hyperbolic geometry, however, rigorous mathematical treatment of this model can quickly become mathematically challenging. In this thesis, we improve upon the understanding of hyperbolic random graphs by studying its structural and algorithmical properties. Our main contribution is threefold. First, we analyze the emergence of cliques in this model. We find that whenever the power law exponent β is 2 < β < 3, there exists a clique of polynomial size in n. On the other hand, for β >= 3, the size of the largest clique is logarithmic; which severely contrasts previous models with a constant size clique in this case. We also provide efficient algorithms for finding cliques if the hyperbolic node coordinates are known. Second, we analyze the diameter, i. e., the longest shortest path in the graph. We find that it is of order O(polylog(n)) if 2 < β < 3 and O(logn) if β > 3. To complement these findings, we also show that the diameter is of order at least Ω(logn). Third, we provide an algorithm for embedding a real-world graph into the hyperbolic plane using only its graph structure. To ensure good quality of the embedding, we perform extensive computational experiments on generated hyperbolic random graphs. Further, as a proof of concept, we embed the Amazon product recommendation network and observe that products from the same category are mapped close together. N2 - Komplexe Netzwerke sind in Natur und Gesellschaft allgegenwärtig. Sie tauchen in unterschiedlichsten Domänen auf, wie zum Beispiel als soziale Netzwerke, biologische Interaktionen oder Kommunikationsnetzwerke. Trotz ihrer verschiedenen Ursprünge haben diese Netzwerke jedoch viele strukturelle Gemeinsamkeiten. So sind die Grade der Knoten typischerweise Pareto-verteilt. Das heißt, der Anteil an Knoten mit k Nachbarn ist proportional zu k-ß , wobei ß eine beliebige Konstante ist. Weiterhin haben solche Netzwerke einen hohen Clusterkoezienten, was bedeutet, dass zwei benachbarte Knoten viele gemeinsame Nachbarn haben. Um das Verhalten solcher Netzwerke mathematisch zu studieren, werden sie häug als Zufallsgraphen modelliert. Klassische Modelle wie inhomogene Zufallsgraphen oder das Preferential-Attachment-Modell erzeugen Graphen mit Pareto-verteilten Knotengraden. Cluster sind darin jedoch häug nicht vorhanden, oder werden durch das Hinzufügen unnatürlicher Strukturen künstlich erzeugt. Hyperbolische Zufallsgraphen lösen dieses Problem, indem sie dem Graphen eine Geometrie zugrunde legen. Jeder Knoten erhält hyperbolische Koordinaten, und zwei Knoten sind verbunden, wenn ihre hyperbolische Distanz klein ist. Cluster entstehen dann natürlich, da benachbarte Knoten samt ihrer Nachbarschaften in der Geometrie nah beieinander liegen, und die Pareto-Verteilung der Knotengrade folgt aus der expo- nentiellen Expansion des hyperbolischen Raumes. Durch die hyperbolische Geometrie wird jedoch auch die mathematische Analyse des Modells schnell kompliziert. In dieser Arbeit studieren wir die strukturellen und algorithmischen Eigenschaften von hyperbolischen Zufallsgraphen. Wir beginnen mit der Analyse von Cliquen. Wir beobachten, dass wenn der Pareto-Exponent ß zwischen 2 und 3 liegt, es Cliquen von polynomieller Größe in n gibt. Mit ß > 3 ist die größte Clique noch logarithmisch groß, was früheren Modellen mit konstanter Cliquengröße stark widerspricht. Wir geben auch einen ezienten Algorithmus zur Cliquenndung an, wenn die Koordinaten der Knoten bekannt sind. Als Zweites analysieren wir den Durchmesser, also den längsten kürzesten Pfad in hyperbolischen Zufallsgraphen. Wir beweisen, dass er O (log 3-ß n) lang ist, wenn 2 < ß < 3, und O (log n) falls ß > 3. Komplementär dazu zeigen wir, dass der Durchmesser mindestens Q(log n) beträgt. Als Drittes entwickeln wir einen Algorithmus, der reale Netzwerke in die hyperbolische Ebene einbettet. Um eine gute Qualität zu gewährleisten, evaluieren wir den Algorithmus auf über 6000 zufällig generierten hyperbolischen Graphen. Weiterhin betten wir exemplarisch den Produktempfehlungsgraphen von Amazon ein und beobachten, dass Produkte aus gleichen Kategorien in der Einbettung nah beieinander liegen. KW - random graphs KW - power law KW - massive networks KW - hyperbolic random graphs KW - Zufallsgraphen KW - Pareto-Verteilung KW - gigantische Netzwerke KW - hyperbolische Zufallsgraphen Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-395974 ER -