Abstract. In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition matrix existence results are presented as well

approach to extracting information from Monte Carlo simulations that uses the matrix of transition probabilities. Combining the Transition Matrix with an N-fold way simulation technique produces an extremely flexible and efficient approach to rather general Monte Carlo simulations. 1 1

Abstract. This article represents a major step in the unification of the theory of algebraic, topological and singular transition matrices by introducing a definition which is a generalization that encompasses all of the previous three. When this more general transition matrix satisfies

. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected number of distinct hidden states in a finite

We present a generalization of topological transition matrices introduced in [6]. 1.

Polynomial Functions with non-negative coefficients

Organizations track systems over time. Usually static reports are generated monthly, yearly or quarterly, and the reports are compared across time. On the reports are categories of information, usually counts, and other information. Objects in the population may change status over time. They might be added to the inventory, discharged from treatment, or moved within the system. Children graduate from grade school to middle school, stock is moved from warehouse to store shelf, patients improve from hospital to outpatient care. When analyzing a population of such objects it is useful to not just consider the categorical counts, but the change of the population

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss

Abstract ⎯ This paper is concerned with deriving, using logistic and Markov chain theoretic methodologies, a transition matrix for a multi-echelon educational system. The explanatory variables of the logistic model are the school differential variables, and the transition matrix of the Markov chain

stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient