Valuation equilibrium

We introduce a new solution concept for games in extensive form with perfect information, valuation equilibrium, which is based on a partition of each player's moves into similarity classes. A valuation of a player'is a real-valued function on the set of her similarity classes. In this equilibrium each player's strategy is optimal in the sense that at each of her nodes, a player chooses a move that belongs to a class with maximum valuation. The valuation of each player is consistent with the strategy profile in the sense that the valuation of a similarity class is the player's expected payoff, given that the path (induced by the strategy profile) intersects the similarity class. The solution concept is applied to decision problems and multi-player extensive form games. It is contrasted with existing solution concepts. The valuation approach is next applied to stopping games, in which non-terminal moves form a single similarity class, and we note that the behaviors obtained echo some biases observed experimentally. Finally, we tentatively suggest a way of endogenizing the similarity partitions in which moves are categorized according to how well they perform relative to the expected equilibrium value, interpreted as the aspiration level

Querying Probabilistic Neighborhoods in Spatial Data Sets Efficiently

$\newcommand{\dist}{\operatorname{dist}}$ In this paper we define the notion of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in $\mathbb{R}^d$, a query point $q \in \mathbb{R}^d$, a distance metric \dist, and a monotonically decreasing function $f : \mathbb{R}^+ \rightarrow [0,1]$ be given. Then a point $p \in P$ belongs to the probabilistic neighborhood $N(q, f)$ of $q$ with respect to $f$ with probability f(\dist(p,q)). We envision applications in facility location, sensor networks, and other scenarios where a connection between two entities becomes less likely with increasing distance. A straightforward query algorithm would determine a probabilistic neighborhood in $\Theta(n\cdot d)$ time by probing each point in $P$. To answer the query in sublinear time for the planar case, we augment a quadtree suitably and design a corresponding query algorithm. Our theoretical analysis shows that -- for certain distributions of planar $P$ -- our algorithm answers a query in $O((|N(q,f)| + \sqrt{n})\log n)$ time with high probability (whp). This matches up to a logarithmic factor the cost induced by quadtree-based algorithms for deterministic queries and is asymptotically faster than the straightforward approach whenever $|N(q,f)| \in o(n / \log n)$. As practical proofs of concept we use two applications, one in the Euclidean and one in the hyperbolic plane. In particular, our results yield the first generator for random hyperbolic graphs with arbitrary temperatures in subquadratic time. Moreover, our experimental data show the usefulness of our algorithm even if the point distribution is unknown or not uniform: The running time savings over the pairwise probing approach constitute at least one order of magnitude already for a modest number of points and queries.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-44543-4_3

Sr0.9_{0.9}K0.1_{0.1}Zn1.8_{1.8}Mn0.2_{0.2}As2_{2}: a ferromagnetic semiconductor with colossal magnetoresistance

A bulk diluted magnetic semiconductor (Sr,K)(Zn,Mn)$_{2}$As$_{2}$ was synthesized with decoupled charge and spin doping. It has a hexagonal CaAl$_{2}$Si$_{2}$-type structure with the (Zn,Mn)$_{2}$As$_{2}$ layer forming a honeycomb-like network. Magnetization measurements show that the sample undergoes a ferromagnetic transition with a Curie temperature of 12 K and \revision{magnetic moment reaches about 1.5 $\mu_{B}$/Mn under $\mu_0H$ = 5 T and $T$ = 2 K}. Surprisingly, a colossal negative magnetoresistance, defined as $[\rho(H)-\rho(0)]/\rho(0)$, up to $-$38\% under a low field of $\mu_0H$ = 0.1 T and to $-$99.8\% under $\mu_0H$ = 5 T, was observed at $T$ = 2 K. The colossal magnetoresistance can be explained based on the Anderson localization theory.Comment: Accepted for publication in EP

Multi-Step Processing of Spatial Joins

Spatial joins are one of the most important operations for combining spatial objects of several relations. In this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the following two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaining candidates has to be tested against the join predicate. The time required for computing spatial join predicates can essentially be reduced when objects are adequately organized in main memory. In our approach, objects are first decomposed into simple components which are exclusively organized by a main-memory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors

On d*-Complete Topological Spaces and Related Fixed Point Results

In this paper, we introduce the concept ofd*-complete topological spaces, which include earlier defined classes of complete metric spaces and quasib-metric spaces. Further, we prove some fixed point results for mappings defined ond*-complete topological spaces, generalizing earlier results of Taskovic, Ciric and Presic, Presic, Bryant, Marjanovic, Yen, Caccioppoli, Reich and Bianchini

On d*-Complete Topological Spaces and Related Fixed Point Results

In this paper, we introduce the concept ofd*-complete topological spaces, which include earlier defined classes of complete metric spaces and quasib-metric spaces. Further, we prove some fixed point results for mappings defined ond*-complete topological spaces, generalizing earlier results of Taskovic, Ciric and Presic, Presic, Bryant, Marjanovic, Yen, Caccioppoli, Reich and Bianchini