Kinetic transport equations with a given confining potential and non-linear relaxation type collision operators are considered. General (monotone) energy dependent equilibrium distributions are allowed with a chemical potential ensuring mass conservation. Existence and uniqueness of solutions is proven for initial data bounded by equilibrium distributions. The diffusive macroscopic limit is car...

We present a semi-supervised incremental learning algorithm for evolving visual data in order to develop a robust and flexible track classification system in a multi camera surveillance scenario. Most existing methods, which are variations on static learning schemes, can not cope with many real-life challenges. The scarcity of labelled data in real applications ends up generating poor classifie...

The classical drift-diffusion model employed in semi-conductor simulation is now seen as part of a hierarchy of mathematical models designed to capture the intricate patterns of current flow in solid-state devices. These models include those incorporating quantum mechanical effects. Scientific computation has vastly outpaced our mathematical understanding of these models. This article is restri...

We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems In particular we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a drift bifurcation To do this we use results of Arnold to analyze parametrized families of elements ...

We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems. In particular, we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a `drift bifurcation'. To do this, we use results of Arnold to analyze parametrized families of ele...

We present a simple algorithm for clustering semantic patterns based on distributional similarity and use cluster memberships to guide semi-supervised pattern discovery. We apply this approach to the task of relation extraction. The evaluation results demonstrate that our novel bootstrapping procedure significantly outperforms a standard bootstrapping. Most importantly, our algorithm can effect...

In this article, our goal is to prove the existence and uniqueness of solution for 1D and 2D semi-linear hyperbolic equations in a bounded domain with a monotone nonlinear term. We use elliptic regularization and a finite difference scheme in time to build the approximate solutions for the semi-linear hyperbolic equations, and we utilize the regularization method together with the monotonicity ...

Methods for noise cleaning have great significance in classification tasks and in situations when it is necessary to carry out a semi-supervised learning due to importance of having well-labeled samples (prototypes) for classification of the new patterns. In this work, we present a new algorithm for detecting noise in data streams that takes into account changes in concepts over time (concept d...

We consider the problem of function estimation in the case where an underlying causal model can be inferred. This has implications for popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning. We argue that causal knowledge may facilitate some approaches for a given problem, and rule out others. In particular, we formulate a hypothesis for when se...