School of thought analysis is an important yet not-well-elaborated scientific knowledge discovery task. This paper makes the first attempt at this problem. We focus on one aspect of the problem: do characteristic school-of-thought words exist and whether they are characterizable? To answer these questions, we propose a probabilistic generative School-Of-Thought (SOT) model to simulate the scien...

Hertrampf's locally de nable acceptance types show that many complexity classes can be de ned in terms of polynomial time bounded NTM's with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce a modi cation of Hertrampf's locally de nable acceptance types which allows to get a larger number of characterizable...

Hertrampf’s locally definable acceptance types show that many complexity classes can be defined in terms of polynomial time bounded NTM’s with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce a modification of Hertrampf’s locally definable acceptance types which allows to get a larger number of characteriz...

Hertrampf's locally de nable acceptance types show that many complexity classes can be de ned in terms of polynomial time bounded NTM's with simple local conditions on the nodes of its computation tree, rather than global concepts like number of accepting paths etc. We introduce a modi cation of Hertrampf's locally de nable acceptance types which allows to get a larger number of characterizable...

Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident...

let $g$ be a finite group and $pi(g)$ be the set of all the prime‎ ‎divisors of $|g|$‎. ‎the prime graph of $g$ is a simple graph‎ ‎$gamma(g)$ whose vertex set is $pi(g)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $g$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎the degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...

It is well known that there is a one-to-one correspondence between the entropy vector of a collection of n random variables and a certain group-characterizable vector obtained from a finite group and n of its subgroups [1]. However, if one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al [2] that lin...

Function distinguishable languages were introduced as a new methodology of defining characterizable subclasses of the regular languages which are learnable from text. Here, we give details on the implementation and the analysis of the corresponding learning algorithms. We also discuss problems which might occur in practical applications.

-Using Generalized Harmonic Analysis, a complete description of parameter convergence in Model Reference Adaptive Control (MRAC) is given in terms of the spectrum of the exogenous reference input signal. Roughly speaking, if the reference signal "contains enough frequencies" then the parameter vector converges to its correct value. If not, it converges to an easily characterizable subspace in p...