Let G be a finite group, and X a subset of G. The Cayley graph of G with respect to X , written Cay(G,X) has two different definitions in the literature. The vertex set of this graph is the group G. In one definition, there is an arc from g to xg for all g ∈ G and x ∈ X ; in the other definition, for the same pairs (g,x), there is an arc from g to gx. Cayley graphs are generalised by coset grap...

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

Aktract-Construction of efficient block-encoded M-ary phase shift keying (M-PSK) schemes is investigated in this paper. An algebraic approach is adopted in which the basic modulation signals are associated with the elements of a finite group. Using some of the properties of group partition chains, the algebraic properties of linear codes are investigated. From this analysis, a class of codes ca...

Generalized abelian coset conformal field theories. Abstract Primary fields and correlation functions of an arbitrary abelian coset conformal field theory are explicitly expressed in terms of the associated W algebra and u(1) d currents.The coset theory has global abelian symmetry. In this paper we study conformal field theories based on the generalized coset construction [1-3] K(m) = L(m) − L ...

Abstract — Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binaryinput/symmetric-output channels. The case of nonsymmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the b...

Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the performanc...

We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric E8 gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symm...

Another way to do this is to use individual elements. Take an element from {2, 6} and an element from {3, 7} and add them. Find the coset that contains the sum. That coset is the sum of the cosets. For example, if I use 6 from {2, 6} and 3 from {3, 7}, I get 6 + 3 = 1, which is in {1, 5}. Therefore, {2, 6}+ {3, 7} = {1, 5}. What happens if you choose different elements? Take 2 from {2, 6} and 7...

These working notes summarize the different approaches we have explored in order to classify a corpus of tweets related to the 2015 Spanish General Election (COSET 2017 task from IberEval 2017). Two approaches were tested during the COSET 2017 evaluations: Neural Networks with Sentence Embeddings (based on TensorFlow) and N-gram Language Models (based on SRILM). Our results with these approache...