Intersecting Faces: Non-negative Matrix Factorization With New Guarantees

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where provably correct algorithms have been developed. In this paper, we propose the notion of subset-separable NMF, which substantially generalizes the property of separability. We show that subset-separability is a natural necessary condition for the factorization to be unique or to have minimum volume. We developed the Face-Intersect algorithm which provably and efficiently solves subset-separable NMF under natural conditions, and we prove that our algorithm is robust to small noise. We explored the performance of Face-Intersect on simulations and discuss settings where it empirically outperformed the state-of-art methods. Our work is a step towards finding provably correct algorithms that solve large classes of NMF problems

Potential of Hydrodynamic Metamaterial Cloak for Drag Reduction

Metamaterials are rationally designed artificial materials composed of tailored functional building blocks densely packed into an effective material. While metamaterials historically are primarily thought to be associated with negative index of refraction and invisibility cloaking in electromagnetism or optics, it turns out that the simple metamaterial concept also applies to many other areas of physics namely the thermodynamics, classical mechanics including elastostatics, acoustics, fluid dynamics and elastodynamics, and in principle also to the quantum mechanics. The goal of this thesis is to introduce and evaluate the potential of a hydrodynamic metamaterial cloak for drag reduction of objects in viscous flow. In recent years, the hydrodynamic metamaterial cloak has been created in very low Reynolds number Stokes flow by changing the viscosity tensor distribution in the cloak around the object. In practice, the spatially varying viscosity distribution is achieved by introducing a large number of micro-pillars in the cloak domain. In this thesis, the hydrodynamic cloaks for 2D objects of complex shapes such as airfoil are created by coordinate transformation using the Stokes equations for low Reynolds number flows. First, the viscosity tensor for a circular cylinder cloak is derived by coordinate transformation based on the Stokes equations. Then the viscosity tensors for an elliptic-cylinder cloak and an airfoil cloak are obtained by stretching the circular cylinder cloak. The effect of the cloaks is simulated using the commercially available software ANSYS FLUENT 2019R2. The unstructured meshes for all cases are generated by the software ICEM. By comparing the velocity fields, pressure fields, streamlines and wall skin friction coefficient in flow about various geometries without and with cloak, the potential of a hydrodynamic metamaterial cloak for drag reduction is evaluated. The cloak changes the velocity field and pressure field in the cloak region such that the velocity distribution in the region outside the cloak becomes more uniform, and the pressure difference between the upstream and downstream regions of the object becomes smaller; this produces the hydrodynamic hiding effect and drag reduction. These effects are reduced at higher Reynolds numbers. The results for a cloak around a circular cylinder, an elliptic-cylinder, an airfoil and a flat plate (normal to the flow) show that a hydrodynamic cloak has the effect of hiding the object and reduces the drag, although these effects are reduced at high Reynolds numbers

Health Care System Reform in China: Issues, Challenges and Options

This paper examines health care reform in urban and rural China. Before health care reform, Chinese health service facilities were run entirely by the state and basically they performed a social welfare function. This health care system greatly improved the population health conditions but many problems started to emerge in 1980s when the economic reform started. Since then, the government has been struggling to maintain a balance between meeting people¡¯s health care needs and develop the health care "industry". Problems and their contribution factors in organization, financing and performance of the health care reform are examined and analyzed. In terms of organization, decentralization of the decision making power in health sector and marketization of the medical establishments constitutes the main organizational changes in the health care reform. This organizational reform of health sector as an imposed institution change, encounters lots of resistance in the process of implementation. A tremendous amount of conflictions arises because of the commercialization of health sector that used to perform social welfare function. In terms of financing, share of organized financing (government and social fund) in the total health expenditure declined dramatically since the reform. In urban China, Health care insurance faced tough going on universal access. In rural China, there are lots of problems in implementing new cooperative health system partly because of its imperfect design. In terms of performance, data shows that there is growing inequity in health status between rural and urban in the past 15 years. Inefficiencies also exists in both resource allocation and service delivery. Several options are analyzed for organizational reform and health care financing. The report recommends that the aims of the future reform policy that government would adopt should be to improve the population health status instead of generating profit for institutions or industry. The social welfare function of health care system should be reinforced and at the same time managed competition in the health care market should be encouraged. In health care financing in urban area, several directions of broadening risk pooling are discussed. In rural health care financing, the designing of new cooperative health care system is analyzed. Rural financing should be more flexible in order to attract more people to join the cooperative medical system. It is recommended that Chinese government should increase funding for public health programs and subsidize health services for the disadvantaged groups.

Dynamics of a Leslie-Gower predator-prey system with cross-diffusion

A Leslie–Gower predator–prey system with cross-diffusion subject to Neumann boundary conditions is considered. The global existence and boundedness of solutions are shown. Some sufficient conditions ensuring the existence of nonconstant solutions are obtained by means of the Leray–Schauder degree theory. The local and global stability of the positive constant steady-state solution are investigated via eigenvalue analysis and Lyapunov procedure. Based on center manifold reduction and normal form theory, Hopf bifurcation direction and the stability of bifurcating timeperiodic solutions are investigated and a normal form of Bogdanov–Takens bifurcation is determined as well

Asymptotic behavior of solutions to chemical reaction-diffusion systems

International audienceThis paper concerns the study of the asymptotic behavior of solutions to reaction-diffusion systems modelling multi-components reversible chemistry with spatial diffusion. By solution, we understand any limit of adequate approximate solutions. It is proved in any space dimension that, as time tends to infinity, the solution converges exponentially to the unique homogeneous stationary solution. We adapt and extend to any number of components, the entropy decay estimates which have been exploited for some particular 3 × 3 and 4 × 4 systems