Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes

The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian L\'evy processes, however, it is difficult to obtain explicit forms of Fokker-Planck equations because the adjoint operators of the associated infinitesimal generators usually do not have exact formulation. In the present paper, Fokker- Planck equations are derived in terms of infinite series for nonlinear stochastic differential equations with non-Gaussian L\'evy processes. A few examples are presented to illustrate the method.Comment: 14 page

Hierarchical Cross-Modal Talking Face Generationwith Dynamic Pixel-Wise Loss

We devise a cascade GAN approach to generate talking face video, which is robust to different face shapes, view angles, facial characteristics, and noisy audio conditions. Instead of learning a direct mapping from audio to video frames, we propose first to transfer audio to high-level structure, i.e., the facial landmarks, and then to generate video frames conditioned on the landmarks. Compared to a direct audio-to-image approach, our cascade approach avoids fitting spurious correlations between audiovisual signals that are irrelevant to the speech content. We, humans, are sensitive to temporal discontinuities and subtle artifacts in video. To avoid those pixel jittering problems and to enforce the network to focus on audiovisual-correlated regions, we propose a novel dynamically adjustable pixel-wise loss with an attention mechanism. Furthermore, to generate a sharper image with well-synchronized facial movements, we propose a novel regression-based discriminator structure, which considers sequence-level information along with frame-level information. Thoughtful experiments on several datasets and real-world samples demonstrate significantly better results obtained by our method than the state-of-the-art methods in both quantitative and qualitative comparisons

Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty

A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time scale separation. To illustrate this dimension reduction procedure, the impact of random environmental fluctuations on the settling motion of inertial particles in a cellular flow field is examined. It is found that noise delays settling for some particles but enhances settling for others. A deterministic stable manifold is an agent to facilitate this phenomenon. Overall, noise appears to delay the settling in an averaged sense.Comment: 27 pages, 9 figure

Evolution of the Chern-Simons Vortices

Based on the gauge potential decomposition theory and the $\phi$-mapping theory, the topological inner structure of the Chern-Simons-Higgs vortex has been showed in detail. The evolution of CSH vortices is studied from the topological properties of the Higgs scalar field. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the scalar field $\phi .$Comment: 10 pages, 10 figure

A hydrodynamic study of a fast‐bed dual circulating fluidized bed for chemical looping combustion

This study explores the use of a dual interconnected circulating fluidized bed (CFB) for chemical looping combustion. This design can enhance gas–solid interactions, but it is difficult to control the solid transfer and circulation rates. With the use of a 1:1 scale cold-flow model, an investigation determining the hydrodynamic behavior of the dual CFB system has been conducted. The cold-flow system consists of two identical fast-bed risers, each with an internal diameter of 100 mm and a height of 7 m. The simplified cold-flow model is based on the chemical looping Pilot-Scale Advanced CO2 Capture Technology (PACT) facility at Cranfield. Here, we have determined the minimum fluidization and transport velocities, and we have assessed the solid density profiles, transport capacity, and potential for the dilution by air/N2 leakage into the CO2 stream exiting the fuel reactor. The experimental procedure uses two different bed materials, molochite (ceramic clay) and FE100 (iron particles), and it satisfies the dynamic scaling laws to model the bed inventory within the system. The results indicate that the two fast-bed risers share similar density and pressure profiles. Stable circulation can be achieved through pneumatic transport. The circulation rate of the system is flexible and can be adjusted by altering the fluidization velocity in the riser and by altering the bed inventory. The gas leakage from the loop seal to the cyclone was found to be sensitive to the bed height and fluidization velocity in the loop seal. However, by maintaining a loop-seal bed height above 600 mm during operation, the outlet stream remains undiluted

A computer vision approach to classification of birds in flight from video sequences

Bird populations are an important bio-indicator; so collecting reliable data is useful for ecologists helping conserve and manage fragile ecosystems. However, existing manual monitoring methods are labour-intensive, time-consuming, and error-prone. The aim of our work is to develop a reliable system, capable of automatically classifying individual bird species in flight from videos. This is challenging, but appropriate for use in the field, since there is often a requirement to identify in flight, rather than when stationary. We present our work in progress, which uses combined appearance and motion features to classify and present experimental results across seven species using Normal Bayes classifier with majority voting and achieving a classification rate of 86%

The emerging roles and therapeutic potential of cyclin-dependent kinase 11 (CDK11) in human cancer.

Overexpression and/or hyperactivation of cyclin-dependent kinases (CDKs) are common features of most cancer types. CDKs have been shown to play important roles in tumor cell proliferation and growth by controlling cell cycle, transcription, and RNA splicing. CDK4/6 inhibitor palbociclib has been recently approved by the FDA for the treatment of breast cancer. CDK11 is a serine/threonine protein kinase in the CDK family and recent studies have shown that CDK11 also plays critical roles in cancer cell growth and proliferation. A variety of genetic and epigenetic events may cause universal overexpression of CDK11 in human cancers. Inhibition of CDK11 has been shown to lead to cancer cell death and apoptosis. Significant evidence has suggested that CDK11 may be a novel and promising therapeutic target for the treatment of cancers. This review will focus on the emerging roles of CDK11 in human cancers, and provide a proof-of-principle for continued efforts toward targeting CDK11 for effective cancer treatment