@article{2178,
abstract = {We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time T, the size of the design matrix is 6 × 3 · 2T-1 and the convex hull of its columns is the model polytope. We study the behavior of this polytope for T ≥ 3 and we show that it is defined by 24 facets for all T ≥ 5. Moreover, we give a complete description of these facets. From this, we deduce that the toric ideal associated with the design matrix is generated by binomials of degree at most 6. Our proof is based on a result due to Sturmfels, who gave a bound on the degree of the generators of a toric ideal, provided the normality of the corresponding toric variety. In our setting, we established the normality of the toric variety associated to the THMC model by studying the geometric properties of the model polytope.},
author = {Haws, David and Martin Del Campo Sanchez, Abraham and Takemura, Akimichi and Yoshida, Ruriko},
journal = {Beitrage zur Algebra und Geometrie},
number = {1},
pages = {161 -- 188},
publisher = {Springer},
title = {{Markov degree of the three-state toric homogeneous Markov chain model}},
doi = {10.1007/s13366-013-0178-y},
volume = {55},
year = {2014},
}
@article{2179,
abstract = {We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.},
author = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H},
journal = {Electronic Communications in Probability},
publisher = {Institute of Mathematical Statistics},
title = {{Local semicircle law with imprimitive variance matrix}},
doi = {10.1214/ECP.v19-3121},
volume = {19},
year = {2014},
}
@article{2180,
abstract = {Weighted majority votes allow one to combine the output of several classifiers or voters. MinCq is a recent algorithm for optimizing the weight of each voter based on the minimization of a theoretical bound over the risk of the vote with elegant PAC-Bayesian generalization guarantees. However, while it has demonstrated good performance when combining weak classifiers, MinCq cannot make use of the useful a priori knowledge that one may have when using a mixture of weak and strong voters. In this paper, we propose P-MinCq, an extension of MinCq that can incorporate such knowledge in the form of a constraint over the distribution of the weights, along with general proofs of convergence that stand in the sample compression setting for data-dependent voters. The approach is applied to a vote of k-NN classifiers with a specific modeling of the voters' performance. P-MinCq significantly outperforms the classic k-NN classifier, a symmetric NN and MinCq using the same voters. We show that it is also competitive with LMNN, a popular metric learning algorithm, and that combining both approaches further reduces the error.},
author = {Bellet, Aurélien and Habrard, Amaury and Morvant, Emilie and Sebban, Marc},
journal = {Machine Learning},
number = {1-2},
pages = {129 -- 154},
publisher = {Springer},
title = {{Learning a priori constrained weighted majority votes}},
doi = {10.1007/s10994-014-5462-z},
volume = {97},
year = {2014},
}
@article{2183,
abstract = {We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be nontrivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: Nodes can be divided in differently synchronized classes but, contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behavior can evolve from undifferentiated nodes.},
author = {Botella Soler, Vicente and Glendinning, Paul},
journal = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
number = {6},
publisher = {American Institute of Physics},
title = {{Hierarchy and polysynchrony in an adaptive network }},
doi = {10.1103/PhysRevE.89.062809},
volume = {89},
year = {2014},
}
@article{2184,
abstract = {Given topological spaces X,Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X→ Y. We consider a computational version, where X,Y are given as finite simplicial complexes, and the goal is to compute [X,Y], that is, all homotopy classes of suchmaps.We solve this problem in the stable range, where for some d ≥ 2, we have dim X ≤ 2d-2 and Y is (d-1)-connected; in particular, Y can be the d-dimensional sphere Sd. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools from effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X,Y] is known to be uncomputable for general X,Y, since for X = S1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, and extended to other problems, such as the extension problem, where we are given a subspace A ⊂ X and a map A→ Y and ask whether it extends to a map X → Y, or computing the Z2-index-everything in the stable range. Outside the stable range, the extension problem is undecidable.},
author = {Čadek, Martin and Krcál, Marek and Matoušek, Jiří and Sergeraert, Francis and Vokřínek, Lukáš and Wagner, Uli},
journal = {Journal of the ACM},
number = {3},
publisher = {ACM},
title = {{Computing all maps into a sphere}},
doi = {10.1145/2597629},
volume = {61},
year = {2014},
}