In this paper, a global methodology for the long-term prediction of time series is proposed. This methodology combines direct prediction strategy and sophisticated input selection criteria: k-nearest neighbors approximation method (k-NN), mutual information (MI) and nonparametric noise estimation (NNE). A global input selection strategy that combines forward selection, backward elimination (or pruning) and forward-backward selection is introduced. This methodology is used to optimize the three input selection criteria (k-NN, MI and NNE). The methodology is successfully applied to a real life benchmark: the Poland Electricity Load dataset.

We consider the stochastic matching problem. An edge-weighted general (i.e., not necessarily bipartite) graph G(V, E) is given in the input, where each edge in E is realized independently with probability p; the realization is initially unknown, however, we are able to query the edges to determine whether they are realized. The goal is to query only a small number of edges to find a realized matching that is sufficiently close to the maximum matching among all realized edges. This problem has received a considerable attention during the past decade due to its numerous real-world applications in kidney-exchange, matchmaking services, online labor markets, and advertisements.Our main result is an adaptive algorithm that for any arbitrarily small > 0, finds a (1 − )approximation in expectation, by querying only O(1) edges per vertex. We further show that our approach leads to a (1/2 − )-approximate non-adaptive algorithm that also queries only O(1) edges per vertex. Prior to our work, no nontrivial approximation was known for weighted graphs using a constant per-vertex budget. The state-of-the-art adaptive (resp. non-adaptive) algorithm of Maehara and Yamaguchi [SODA 2018] achieves a (1− )-approximation (resp. (1/2− )-approximation) by querying up to O(w log n) edges per vertex where w denotes the maximum integer edge-weight. Our result is a substantial improvement over this bound and has an appealing message: No matter what the structure of the input graph is, one can get arbitrarily close to the optimum solution by querying only a constant number of edges per vertex.To obtain our results, we introduce novel properties of a generalization of augmenting paths to weighted matchings that may be of independent interest. * A preliminary version of this paper appeared at EC 2018. † Portions of this work were completed while the author was an intern at Upwork.

Abstract. This paper presents a comparison between direct and recursive prediction strategies. In order to perform the input selection, an approach based on mutual information is used. The mutual information is computed between all the possible input sets and the outputs. Least Squares Support Vector Machines are used as non-linear models to avoid local minima problems. Results are illustrated on the Poland electricity load benchmark and they show the superiority of the direct prediction strategy.

We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph G = (V, E) along with a parameter p ∈ (0, 1) is given in the input. Each edge of G is realized independently with probability p. The goal is to select a degree bounded (dependent only on p) subgraph H of G such that the expected size/weight of maximum realized matching of H is close to that of G.This model of stochastic matching has attracted significant attention over the recent years due to its various applications in kidney exchange, online labor markets, and other matching markets.The most fundamental open question is the best approximation factor achievable for such algorithms that, in the literature, are referred to as non-adaptive algorithms. Prior work has identified breaking (near) half-approximation as a barrier for both weighted and unweighted graphs. Our main results are as follows:• We analyze a simple and clean algorithm and show that for unweighted graphs, it finds an (almost) 4 √ 2 − 5 (≈ 0.6568) approximation by querying O( log(1/p) p ) edges per vertex. This improves over the state-of-the-art 0.5001 approximation of Assadi et al. [EC'17].• We show that the same algorithm achieves a 0.501 approximation for weighted graphs by querying O( log(1/p) p ) edges per vertex. This is the first algorithm to break 0.5 approximation barrier for weighted graphs. It also improves the per-vertex queries of the state-ofthe-art by Yamaguchi and Maehara [SODA'18] and Behnezhad and Reyhani [EC'18].Prior results were all interestingly based on similar algorithms and differed only in the analysis. Our algorithms are fundamentally different, yet very simple and natural. For the analysis, we introduce a number of procedures that construct heavy fractional matchings. We consider the new algorithms and our analytical tools to be the main contributions of this paper. * Portion of the work was completed while some of the authors were at

Colorectal cancer (CRC) is the second most common cause of cancer-related deaths in the Western world and interactions between genetic and environmental factors, including diet, are suggested to play a critical role in its etiology. We conducted a long-term feeding experiment in the mouse to address gene expression and methylation changes arising in histologically normal colonic mucosa as putative cancer-predisposing events available for early detection. The expression of 94 growth-regulatory genes previously linked to human CRC was studied at two time points (5 weeks and 12 months of age) in the heterozygote Mlh1 +/- mice, an animal model for human Lynch syndrome (LS), and wild type Mlh1 +/+ littermates, fed by either Western-style (WD) or AIN-93G control diet. In mice fed with WD, proximal colon mucosa, the predominant site of cancer formation in LS, exhibited a significant expression decrease in tumor suppressor genes, Dkk1, Hoxd1, Slc5a8, and Socs1, the latter two only in the Mlh1 +/- mice. Reduced mRNA expression was accompanied by increased promoter methylation of the respective genes. The strongest expression decrease (7.3 fold) together with a significant increase in its promoter methylation was seen in Dkk1, an antagonist of the canonical Wnt signaling pathway. Furthermore, the inactivation of Dkk1 seems to predispose to neoplasias in the proximal colon. This and the fact that Mlh1 which showed only modest methylation was still expressed in both Mlh1 +/- and Mlh1 +/+ mice indicate that the expression decreases and the inactivation of Dkk1 in particular is a prominent early marker for colon oncogenesis.