Intersection Graph

, M.Sc. Thesis Sharif University of Technology Yaghoobian, Maysam (Author) ; Akbari, Saeed (Supervisor)

Abstract

Let R be a ring with unity, M be a unitary left R-module and I(M)* be the set of all non-trivial submodules of M. The intersection graph of submodules of M, denoted by G(M), is a graph with the vertex set I(M)* and two distinct vertices N and K are adjacent if and only if N\K ̸= 0. We investigate the interplay between the module-theoretic properties of M and the graph-theoretic properties of G(M). We characterize all modules for which the intersection graph of submodules is connected. Also the diameter and the girth of G(M) are determined. We study the clique number and the chromatic number of G(M). Among other results, it is shown that if G(M) is a bipartite graph, then G(M) is a star...

Hubert Dreyfus on the Impossibility of Artificial Intelligence: Consequences and Implications

, M.Sc. Thesis Sharif University of Technology Aghili Dehkordi, Bamdad (Author) ; Sefidkhosh, Maysam (Supervisor) ; Taqavi, Mostafa ($item.subfieldsMap.e)

Abstract

Hubert Dreyfus other than being a prominent philosopher is amongst early critics of classical artificial intelligence project which was initialized during 1955-1960. Challenging the rationalist presuppositions of this paradigm, he foresaw various situations where mechanical artificial intelligence based upon modeling the world through symbolic representation and mimicking reason by formalized rules would fail to deliver even remotely similar outputs in digital computers as in human though process and problem solving ability.Twenty years later it became obvious for AI researchers that obstacles like frame problem or lack of common sense would follow their projects no matter what computing...

Random Walks on the Mapping Class Group

, M.Sc. Thesis Sharif University of Technology Anvari, Leila (Author) ; Safdari, Mohammad (Supervisor) ; Nassiri, Maysam (Supervisor) ; Talebi, Aminossadat (Co-Supervisor)

Abstract

Let Σ be a connected orientable surface of finite type. Due to Nielsen and Thurston’s classification, it is known that any element of the mapping class group of Σ is periodic, reducible, or (exclusively) pseudo-Anosov. Thus it is natural to form a random walk on the mapping class group with a step distribution and ask about the asymptotic distribution of the location of the random walk on each of the mentioned classes. Joseph Maher has proved that if the group generated by the support of is a non-elementary subgroup of the mapping class group, then the random walk will encounter a pseudo-Anosov element with asymptotic probability one. Indeed, this result not only concerns random walks on...