Invariant Jordan curves of Sierpiski carpet rational maps

In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.Comment: 16 pages, 1 figu

NaI revisited: Theoretical investigation of predissociation via ultrafast XUV transient absorption spectroscopy.

Avoided crossings can trigger abrupt changes of electronic character and redirect the outcomes of photochemical reactions. Here, we report a theoretical investigation into core-level spectroscopic probing of predissociation dynamics of sodium iodide (NaI), a prototype system for studies of avoided-crossing dynamics. The elegant femtochemistry work of Zewail and co-workers pioneered the real-time dynamics of NaI, detecting the Na atoms bursting forth from the avoided crossing and the residual NaI molecules oscillating inside the quasibound potential. The simulated results show that core-level spectroscopy not only observes these integrated outcomes but also provides a direct measure of the abrupt switching of electronic character at the avoided crossing. The valence and core-excited electronic structures of NaI are computed by spin-orbit general multiconfigurational quasidegenerate perturbation theory, from which core-level absorption spectra of the predissociation dynamics are constructed. The wave-packet motion on the covalent potential is continuously mapped as shifts in the absorption energies, and the switching between the covalent and ionic character at the avoided crossing is characterized as the sharp rise and fall of the Na+ signal. The Na+ signal is found to be insensitive to the wave-packet motion in the asymptotic part of the ionic potential, which, in turn, enables a direct measure of the nonadiabatic crossing probability excluding the effect of wave-packet broadening

Coordination of Purchasing and Bidding Activities Across Markets

In both consumer purchasing and industrial procurement, combinatorial interdependencies among the items to be purchased are commonplace. E-commerce compounds the problem by providing more opportunities for switching suppliers at low costs, but also potentially eases the problem by enabling automated market decision-making systems, commonly referred to as trading agents, to make purchasing decisions in an integrated manner across markets. Most of the existing research related to trading agents assumes that there exists a combinatorial market mechanism in which buyers (or sellers) can bid (or sell) service or merchant bundles. Todayâ??s prevailing e-commerce practice, however, does not support this assumption in general and thus limits the practical applicability of these approaches. We are investigating a new approach to deal with the combinatorial interdependency challenges for online markets. This approach relies on existing commercial online market institutions such as posted-price markets and various online auctions that sell single items. It uses trading agents to coordinate a buyerâ??s purchasing and bidding activities across multiple online markets simultaneously to achieve the best overall procurement effectiveness. This paper presents two sets of models related to this approach. The first set of models formalizes optimal purchasing decisions across posted-price markets with fixed transaction costs. Flat shipping costs, a common e-tailing practice, are captured in these models. We observe that making optimal purchasing decisions in this context is NP-hard in the strong sense and suggest several efficient computational methods based on discrete location theory. The second set of models is concerned with the coordination of bidding activities across multiple online auctions. We study the underlying coordination problem for a collection of first or second-price sealed-bid auctions and derive the optimal coordination and bidding policies.

IT and the Environment: An Application in Supply Chain Management

The development of new and improved Information Technology (IT) methods for Supply Chain Management is important. Existing methods suffer from several shortcomings, especially the ability to deal with a mixture of quantitative and qualitative data. This study aims to apply decision support techniques to the area of Supply Chain Management in order to address some of the shortcomings. The methodology follows structuring and modeling. A three-step decision structuring framework is used to develop a model, based on Bayesian networks, to support Supply Chain Management scenarios. The result is a Bayesian network that incorporates the knowledge of experts into a decision support model. It is shown that the model is essential as it contains all the vital elements of the problem from a managerial viewpoint. The described model can be used to perform what-if analysis in various ways, thereby supporting the management of risk in different scenarios. The contribution of this research is not limited to the model, but the study also provides insights into how decision support, and especially Bayesian networks, can enhance IT methods

Clustering Customer Shopping Trips With Network Structure

Moving objects can be tracked with sensors such as RFID tags or GPS devices. Their movement can be represented as sequences of time-stamped locations. Studying such spatio-temporal movement sequences to discover spatial sequential patterns holds promises in many real-world settings. A few interesting applications are customer shopping traverse pattern discovery, vehicle traveling pattern discovery, and route prediction. Traditional spatial data mining algorithms suitable for the Euclidean space are not directly applicable in these settings. We propose a new algorithm to cluster movement paths such as shopping trips for pattern discovery. In our work, we represent the spatio-temporal series as sequences of discrete locations following a pre-defined network. We incorporate a modified version of the Longest Common Subsequence (LCS) algorithm with the network structure to measure the similarity of movement paths. With such spatial networks we implicitly address the existence of spatial obstructs as well. Experiments were performed on both hand-collected real-life trips and simulated trips in grocery shopping. The initial evaluation results show that our proposed approach, called Net-LCSS, can be used to support effective and efficient clustering for shopping trip pattern discovery

Evolutionary dynamics of cryptocurrency transaction networks: An empirical study

Cryptocurrency is a well-developed blockchain technology application that is currently a heated topic throughout the world. The public availability of transaction histories offers an opportunity to analyze and compare different cryptocurrencies. In this paper, we present a dynamic network analysis of three representative blockchain-based cryptocurrencies: Bitcoin, Ethereum, and Namecoin. By analyzing the accumulated network growth, we find that, unlike most other networks, these cryptocurrency networks do not always densify over time, and they are changing all the time with relatively low node and edge repetition ratios. Therefore, we then construct separate networks on a monthly basis, trace the changes of typical network characteristics (including degree distribution, degree assortativity, clustering coefficient, and the largest connected component) over time, and compare the three. We find that the degree distribution of these monthly transaction networks cannot be well fitted by the famous power-law distribution, at the same time, different currency still has different network properties, e.g., both Bitcoin and Ethereum networks are heavy-tailed with disassortative mixing, however, only the former can be treated as a small world. These network properties reflect the evolutionary characteristics and competitive power of these three cryptocurrencies and provide a foundation for future research

Coordination of Purchasing and Bidding Activities Across Markets

In both consumer purchasing and industrial procurement, combinatorial interdependencies among the items to be purchased are commonplace. E-commerce compounds the problem by providing more opportunities for switching suppliers at low costs, but also potentially eases the problem by enabling automated market decision-making systems, commonly referred to as trading agents, to make purchasing decisions in an integrated manner across markets. Most of the existing research related to trading agents assumes that there exists a combinatorial market mechanism in which buyers (or sellers) can bid (or sell) service or merchant bundles. Today’s prevailing e-commerce practice, however, does not support this assumption in general and thus limits the practical applicability of these approaches. We are investigating a new approach to deal with the combinatorial interdependency challenges for online markets. This approach relies on existing commercial online market institutions such as posted-price markets and various online auctions that sell single items. It uses trading agents to coordinate a buyer’s purchasing and bidding activities across multiple online markets simultaneously to achieve the best overall procurement effectiveness. This paper presents two sets of models related to this approach. The first set of models formalizes optimal purchasing decisions across posted-price markets with fixed transaction costs. Flat shipping costs, a common e-tailing practice, are captured in these models. We observe that making optimal purchasing decisions in this context is N P-hard in the strong sense and suggest several efficient computational methods based on discrete location theory. The second set of models is concerned with the coordination of bidding activities across multiple online auctions. We study the underlying coordination problem for a collection of firstor second-price sealed-bid auctions and derive the optimal coordination and bidding policies