DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2017-03-25T05:57:19ZCLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHS
http://hdl.handle.net/10203/220432
Title: CLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHS
Authors: Choi, Suyoung; Masuda, Mikiya; Oum, Sang-il
Abstract: We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism between the real Bott manifolds.
Our characterization can also be described in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors. Finally, we produce some numerical invariants of real Bott manifolds from the viewpoint of graph theory and discuss their topological meaning. As a byproduct, we prove that the toral rank conjecture holds for real Bott manifolds.2017-04-01T00:00:00ZCHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3
http://hdl.handle.net/10203/220445
Title: CHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3
Authors: Baek, Sanghoon
Abstract: We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension 2 Chow groups of a product of Severi-Brauer varieties. In particular, for any n >= 2 we completely determine the degree 3 invariants of a split semisimple group, the quotient of (SL2)(n) by its maximal central sub-group, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.2017-03-01T00:00:00ZColoring graphs without fan vertex-minors and graphs without cycle pivot-minors
http://hdl.handle.net/10203/220433
Title: Coloring graphs without fan vertex-minors and graphs without cycle pivot-minors
Authors: Choi, Ilkyoo; Kwon, O-Joung; Oum, Sang-il
Abstract: A fan F-k is a graph that consists of an induced path on k vertices and an additional vertex that is adjacent to all vertices of the path. We prove that for all positive integers q and k, every graph with sufficiently large chromatic number contains either a clique of size q or a vertex-minor isomorphic to F-k. We also prove that for all positive integers q and k >= 3, every graph with sufficiently large chromatic number contains either a clique of size q or a pivot-minor isomorphic to a cycle of length k. (C) 2016 Elsevier Inc. All rights reserved.2017-03-01T00:00:00ZOptimal Throughput Analysis of Random Access Policies for Cognitive Radio Networks with Multiple Channel Access
http://hdl.handle.net/10203/219022
Title: Optimal Throughput Analysis of Random Access Policies for Cognitive Radio Networks with Multiple Channel Access
Authors: Choi, Jun Kyun; Park, Sangdon; Hwang, Ganguk
Abstract: In this paper we consider a time slotted cognitive radio (CR) network with N wireless channels and M secondary users(SUs). We focus on a random access policy where each SU stochastically decides whether to access idle channels or not based on the given access probability (AP) that is adapted to the channel state information (CSI), if possible. The AP plays an important role in the random access policy because it can control the number of SUs who can access idle channels in a simple manner and hence alleviate packet collisions among SUs. We assume that each SU can access at most L idle channels simultaneously at a time slot whenever possible.
We consider two extreme cases - a) where all SUs have full CSI and b) where all SUs have no CSI. We analyze the throughput of an arbitrary SU for the two extreme cases, and rigorously derive a closed-form expression of the optimal AP values that maximize the throughput of an arbitrary SU for the two extreme cases. In the analysis, we also show the impact of multiple channel access and the acquisition of CSI on throughput performance.2016-12-13T00:00:00Z