Periodic motions with impact chatters in an impact Duffing oscillator.

The periodic motions of discontinuous nonlinear dynamical systems are very difficult problems to solve in engineering and physics. Until now, except for numerical studies, one cannot find a better way to solve such problems. In fact, one still has difficulty obtaining periodic motions in continuous nonlinear dynamical systems.

Enhancing cryo-EM structure prediction with DeepTracer and AlphaFold2 integration.

Understanding the protein structures is invaluable in various biomedical applications, such as vaccine development. Protein structure model building from experimental electron density maps is a time-consuming and labor-intensive task. To address the challenge, machine learning approaches have been proposed to automate this process.

Limit cycles and homoclinic networks in two-dimensional polynomial systems.

In this paper, the properties of equilibriums in planar polynomial dynamical systems are studied. The homoclinic networks of sources, sinks, and saddles in self-univariate polynomial systems are discussed, and the numbers of sources, sinks, and saddles are determined through a theorem, and the first integral manifolds are determined. The corresponding proof of the theorem is completed, and a few illustrations of networks for source, sinks, and saddles are presented for a better understanding of the homoclinic networks.

Constructed complex motions and chaos.

Constructed motions and dynamic topology are new trends in solving nonlinear systems or system interactions. In nonlinear engineering, it is significant to achieve specific complex motions to satisfy expected dynamical behaviors (e.g.

Nonlinear piezoelectric energy harvesting induced through the Duffing oscillator.

In this paper, nonlinear piezoelectric energy harvesting induced by a Duffing oscillator is studied, and the bifurcation trees of period-1 motions to chaos for such a piezoelectric energy-harvesting system are obtained analytically. Distributed-parameter electromechanical modeling of a piezoelectric energy harvester is presented first, and the electromechanically coupled circuit equation excited by infinitely many vibration modes is developed. The governing electromechanical equations are reduced to ordinary differential equations in modal coordinates, and eventually an infinite set of algebraic equations is obtained for the complex modal vibration responses and the complex voltage responses of the energy harvester beam.

Period-3 motions to chaos in a periodically forced nonlinear-spring pendulum.

In this paper, the complete bifurcation dynamics of period-3 motions to chaos are obtained semi-analytically through the implicit mapping method. Such an implicit mapping method employs discrete implicit maps to construct mapping structures of periodic motions to determine complex periodic motions. Analytical bifurcation trees of period-3 motions to chaos are determined through nonlinear algebraic equations generated through the discrete implicit maps, and the corresponding stability and bifurcations of periodic motions are achieved through eigenvalue analysis.

Periodic motions and homoclinic orbits in a discontinuous dynamical system on a single domain with multiple vector fields.

In this paper, periodic motions and homoclinic orbits in a discontinuous dynamical system on a single domain with two vector fields are discussed. Constructing periodic motions and homoclinic orbits in discontinuous dynamical systems is very significant in mathematics and engineering applications, and how to construct periodic motions and homoclinic orbits is a central issue in discontinuous dynamical systems. Herein, how to construct periodic motions and homoclinic orbits is presented through studying a simple discontinuous dynamical system on a domain confined by two prescribed energies.

On infinite homoclinic orbits induced by unstable periodic orbits in the Lorenz system.

In this paper, infinite homoclinic orbits existing in the Lorenz system are analytically presented. Such homoclinic orbits are induced by unstable periodic orbits on bifurcation trees through period-doubling cascades. Each unstable periodic orbit ends at its corresponding homoclinic orbit.

Challenges in the phenotypic characterisation of patients in genetic studies of coronary artery disease.

Coronary artery disease and acute myocardial infarction are complex traits in which there has been recent research to identify the principal genes that engender susceptibility or provide protection. Although there has been exceptional progress in the technology, which now allows genotyping of hundreds of thousands of single-nucleotide polymorphisms in each individual, there remains a pattern of inconsistency in the studies performed to date, in part owing to the difficulties in defining cases and controls. In this paper, salient issues to facilitate research in this important field are reviewed.

Imaging microvascular obstruction and its clinical significance following acute myocardial infarction.

Obstruction of the coronary microvasculature contributes to the pathophysiology of MI and adversely affects post-MI recovery. This "no-reflow" phenomenon resulting from microvascular obstruction is an indicator of lack of adequate tissue perfusion within the infarcted myocardium, even after restoration of epicardial blood flow. Regions of microvascular obstruction can be detected and quantifed because of rapid advances in and refinement of imaging technologies over the past decade.

High-throughput single-nucleotide polymorphisms genotyping: TaqMan assay and pyrosequencing assay.

Single-nucleotide polymorphisms (SNPs) are DNA sequence variations that occur at a single base in the genome sequence. SNPs are valuable markers for identifying genes responsible for susceptibility to common diseases, and in some cases, they are the causes of human diseases. A genetic study of a complex disease usually involves a case-control association study that requires genotyping of a large number of SNPs in hundreds of patients (cases) and matched controls.