Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define parts-based, and linear representation of nonnegative data. Recently, Graph regularized NMF (GrNMF) is proposed to find a compact representation,which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure. In GNMF, an affinity graph is constructed from the original data space to encode the geometrical information. In this paper, we propose a novel idea which engages a Multiple Kernel Learning approach into refining the graph structure that reflects the factorization of the matrix and the new data space. The GrNMF is improved by utilizing the graph refined by the kernel learning, and then a novel kernel learning method is introduced under the GrNMF framework. Our approach shows encouraging results of the proposed algorithm in comparison to the state-of-the-art clustering algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible writin

Bridging the gap between the Jaynes-Cummings and Rabi models using an intermediate rotating wave approximation

We present a novel approach called the intermediate rotating wave approximation (IRWA), which employs a time-averaging method to encapsulate the dynamics of light-matter interaction from strong to ultrastrong coupling regime. In contrast to the ordinary rotating wave approximation, this method addresses the co-rotating and counter-rotating terms separately to trace their physical consequences individually, and thus establishes the continuity between the Jaynes-Cummings model and the quantum Rabi model. We investigate IRWA in near resonance and large detuning cases. Our IRWA not only agrees well with both models in their respective coupling strengths, but also offers a good explanation for their differences

Financial Integration and International Risk Sharing

Conventional wisdom suggests that financial liberalization can help countries insure against idiosyncratic risk. There is little evidence, however, that countries have increased risk sharing despite recent widespread financial liberalization. This work shows that the key to understanding this puzzling observation is that conventional wisdom assumes frictionless international financial markets, while actual international financial markets are far from frictionless. In particular, financial contracts are incomplete and enforceability of debt repayment is limited. Default risk of debt contracts constrains borrowing, and more importantly, it makes borrowing more difficult in bad times, precisely when countries need insurance the most. Thus, default risk of debt contracts hinders international risk sharing. When countries remove their official capital controls, default risk is still present as an implicit barrier to capital flows; the observed increase in capital flows under financial liberalization is in fact too limited to improve risk sharing. If default risk of debt contracts were eliminated, capital flows would be six times greater, and international risk sharing would increase substantially.international risk sharing, financial integration, financial liberalization, financial frictions, sovereign default, international capital flows

Financial Integration and International Risk Sharing

In the last two decades, financial integration has increased dramatically across the world. At the same time, the fraction of countries in default has more than doubled. Contrary to theory, however, there appears to have been no substantial improvement in the degree of international risk sharing. To account for this puzzle, we construct a general equilibrium model that features a continuum of countries and default choices on state-uncontingent bonds. We model increased financial integration as a decrease in the cost of borrowing. Our main finding is that as the cost of borrowing is lowered, financial integration and sovereign default increases substantially, but the degree of risk sharing as measured by cross section and panel regressions increases hardly at all. The explanation, we propose, is that international risk sharing is not sensitive to the increase in financial integration given the current magnitude of capital flows because countries can insure themselves through accumulation of domestic assets. To get better risk sharing, capital flows among countries need to be extremely large. In addition, although the ability to default on loans provides state contingency, it restricts international risk sharing in two ways: higher borrowing rates and future exclusion from international credit marketsFinanical Integration, Risk Sharing, Globalization, Sovereign Debt