In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and tools of Hopf algebras.

Complexity of existing mathematical models inhibits the analysis and the automatic animation of human and animal motion. Current techniques rely on numerical simulations of highly nonlinear differential equations in highdimensional spaces. A motion with such large-scale dynamics is difficult to control because of the sheer size of its control space. We are developing a method for constructing s...

Complexity of existing mathematical models inhibits the analysis and the automatic animation of human and animal motion. Current techniques rely on numerical simulations of highly nonlinear differential equations in highdimensional spaces. A motion with such large-scale dynamics is difficult to control because of the sheer size of its control space. We are developing a method for constructing s...

Model-checking offers a potential for push-button verification. Abstraction is often used to combat the state-space explosion problem and focus the analysis on relevant properties. However, in many such cases, it is difficult to interpret the results of verification on an abstract system with respect to a concrete one. In this paper we present an abstract model-checking approach that guarantees...

We consider the verification of algorithms expressed in the Heard-Of Model, a round-based computational model for fault-tolerant distributed computing. Rounds in this model are communication-closed, and we show that every execution recording individual events corresponds to a coarser-grained execution based on global rounds such that the local views of all processes are identical in the two exe...

Recently, we proposed an autoregressive linear mixed effects model for the analysis of longitudinal data in which the current response is regressed on the previous response, fixed effects, and random effects (Funatogawa et al., Statist. Med. 2007; 26:2113-2130). The model represents profiles approaching random equilibriums. Because intermittent missing is an inherent problem of the autoregressi...

We survey existing approaches to the formal verification of statecharts using model checking. Although the semantics and subset of statecharts used in each approach varies considerably, along with the model checkers and their specification languages, most approaches rely on translating the hierarchical structure into the flat representation of the input language of the model checker. This makes...

We describe a Markov latent state space (MLSS) model, where the latent state distribution is a decaying mixture over multiple past states. We present a simple sampling algorithm that allows to approximate such high-order MLSS with fixed time and memory costs.