The Domingos-Richardson model, along with several other infection models, has a wide range of applications in prediction. In most of these, a fundamental problem arises: the edge infection probabilities are not known. To provide a systematic method for the estimation of these probabilities, the authors have published the Generalized Cascade Model as a general infection framework, and a learning-based method for the solution of the inverse infection problem. In this paper, we will present a case-study of the inverse infection problem. Bankruptcy forecasting, more precisely the prediction of company defaults is an important aspect of banking. We will use 123 A. Bóta et al. our model to predict these bankruptcies that can occur within a three months time frame. The network itself is built from the bank's existing clientele for credit monitoring issues. We have found that using network models for short term prediction, we get much more accurate results than traditional scorecards can provide. We have also improved existing network models by using inverse infection methods for finding the best edge attribute parameters. This improved model was already implemented in August 2013 to OTP Banks credit monitoring process, and since then it has proven its usefulness.

One of the most useful strategies for proving Breaker's win in Maker-Breaker Positional Games is to find a pairing strategy. In some cases there are no pairing strategies at all, in some cases there are unique or almost unique strategies. For the kin a row game, the case k = 9 is the smallest (sharp) for which there exists a Breaker winning pairing (paving) strategy. One pairing strategy for this game was given by Hales and Jewett. In this paper we show that there are other winning pairings for the 9-in-a-row game, all have a very symmetric torus structure. While describing these symmetries we prove that there are only a finite number of non-isomorphic pairings for the game (around 200 thousand), which can be also listed up by a computer program. In addition, we prove that there are no "irregular", non-symmetric pairings. At the end of the paper we also show a pairing strategy for a variant of the 3-dimensional kin a row game.

In Maker-Breaker positional games two players, Maker and Breaker, play on a finite or infinite board with the goal of claiming or preventing the opponent from getting a finite winning set, respectively. For different games there are several winning strategies for Maker or Breaker. One class of winning strategies is the so-called pairing (paving) strategies. Here, we describe all possible pairing strategies for the 9-in-a-row game. Furthermore, we define a graph of the pairings, containing 194,543 vertices and 532,107 edges, in order to give them a structure. A complete characterization of the graph is also given.

No abstract

Abstract. In this paper we define a bridge between pairings and colorings of the hypergraphs by introducing a generalization of pairs called t-cakes for t ∈ N, t ≥ 2. For t = 2 the 2-cakes are the same as the wellknown pairs of system of distinct representatives, that can be turned to pairing strategies in Maker-Breaker hypergraph games, see Hales and Jewett [12]. The two-colorings are the other extremity of t-cakes, in which the whole ground set of the hypergraph is one big cake that we divide into two parts (color classes). Starting from the pairings (2-cake placement) and two-colorings we define the generalized t-cake placements where we pair p elements by q elements (p, q ∈ N, 1 ≤ p, q < t, p + q = t).The method also gives bounds on the condition of winnings in certain biased Chooser-Picker games, which can be introduced similarly to Beck [3]. We illustrate these ideas on the k-in-a-row games for different values of k on the infinite chessboard.