To simplify the optimization of such terms, we would like to carry out the optimization with respect to the density q(u) analytically, so as to remove the dependency on q(u). To this end, we calculate for the optimal variational q∗(u) in the above equation. This approach was suggested in [1], however, it is not well described there. Here we give an extended derivation. A necessary condition for...

This chapter will discuss attempts to produce formal mathematical models for dynamical simulation of the development process of Free/Open Source Software (F/OSS) projects. First, a brief overview for simulation methods of closed source software development is given. Then, based on empirical facts reported in F/OSS case studies, we describe a general framework for F/OSS dynamical simulation mode...

(a) (b) (c) Fig. 7. Models learned with fixed ¯ α from three different walking subjects. (a) The learned latent coordinates shown in blue. (b) − ln variance plot shows smooth high confidence regions, but the variance near data is larger than in Fig.5c, similar to B-GPDM. (c) Typical samples from the dynamic predictive distribution are shown in green, while the mean-prediction sample is shown in...

Methanogenic fermentation involves a natural ecosystem that can be used for waste water treatment. This anaerobic process can have two locally stable steady-states and an unstable one making the process hard to handle. The aim of this work is to propose analytical criteria to detect hazardous working modes, namely situations where the system evolves towards the acidification of the plant. We fi...

This paper presents a dependent multi-output Gaussian process (GP) for modeling complex dynamical systems. The outputs are dependent in this model, which is largely different from previous GP dynamical systems. We adopt convolved multi-output GPs to model the outputs, which are provided with a flexible multi-output covariance function. We adapt the variational inference method with inducing poi...

We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to semantics given in terms of a ring of operators, so that grammatical composition corresponds to operator addition or multiplication. The operators are generators f...

For phoneme classification, this paper describes an acoustic model based on the variational Gaussian process dynamical system (VGPDS). The nonlinear and nonparametric acoustic model is adopted to overcome the limitations of classical hidden Markov models (HMMs) in modeling speech. The Gaussian process prior on the dynamics and emission functions respectively enable the complex dynamic structure...

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size esse...

A new Chemo–Dynamical Smoothed Particle Hydrodynamic (CD-SPH) code is presented. The disk galaxy is described as a multi–fragmented gas and star system, embedded in a cold dark matter halo with a rigid potential field. The star formation (SF) process, SNII, SNIa and PN events, and the chemical enrichment of gas, have all been considered within the framework of the standard SPH model, which we u...

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...