The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation" consists in approximating the stationary behaviour of the stochastic process by the stationary points of the fluid limit. It is known that this may be incorrect in general, as the stationary behaviour of the fluid limit may not be described by its stationary points. We show however that, if the stochastic process is reversible, the fixed point approximation is indeed valid. More precisely, we assume that the stochastic process converges to the fluid limit in distribution (hence in probability) at every fixed point in time. This assumption is very weak and holds for a large family of processes, among which many mean field and other interaction models. We show that the reversibility of the stochastic process implies that any limit point of its stationary distribution is concentrated on stationary points of the fluid limit. If the fluid limit has a unique stationary point, it is an approximation of the stationary distribution of the stochastic process.Comment: 7 pages, preprin

Towards a pivotal-based approach for business process alignment.

This article focuses on business process engineering, especially on alignment between business analysis and implementation. Through a business process management approach, different transformations interfere with process models in order to make them executable. To keep the consistency of process model from business model to IT model, we propose a pivotal metamodel-centric methodology. It aims at keeping or giving all requisite structural and semantic data needed to perform such transformations without loss of information. Through this we can ensure the alignment between business and IT. This article describes the concept of pivotal metamodel and proposes a methodology using such an approach. In addition, we present an example and the resulting benefits

Improving speaker turn embedding by crossmodal transfer learning from face embedding

Learning speaker turn embeddings has shown considerable improvement in situations where conventional speaker modeling approaches fail. However, this improvement is relatively limited when compared to the gain observed in face embedding learning, which has been proven very successful for face verification and clustering tasks. Assuming that face and voices from the same identities share some latent properties (like age, gender, ethnicity), we propose three transfer learning approaches to leverage the knowledge from the face domain (learned from thousands of images and identities) for tasks in the speaker domain. These approaches, namely target embedding transfer, relative distance transfer, and clustering structure transfer, utilize the structure of the source face embedding space at different granularities to regularize the target speaker turn embedding space as optimizing terms. Our methods are evaluated on two public broadcast corpora and yield promising advances over competitive baselines in verification and audio clustering tasks, especially when dealing with short speaker utterances. The analysis of the results also gives insight into characteristics of the embedding spaces and shows their potential applications