Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.Comment: 22 page

Baseline CNN structure analysis for facial expression recognition

We present a baseline convolutional neural network (CNN) structure and image preprocessing methodology to improve facial expression recognition algorithm using CNN. To analyze the most efficient network structure, we investigated four network structures that are known to show good performance in facial expression recognition. Moreover, we also investigated the effect of input image preprocessing methods. Five types of data input (raw, histogram equalization, isotropic smoothing, diffusion-based normalization, difference of Gaussian) were tested, and the accuracy was compared. We trained 20 different CNN models (4 networks x 5 data input types) and verified the performance of each network with test images from five different databases. The experiment result showed that a three-layer structure consisting of a simple convolutional and a max pooling layer with histogram equalization image input was the most efficient. We describe the detailed training procedure and analyze the result of the test accuracy based on considerable observation.Comment: 6 pages, RO-MAN2016 Conferenc

Monomial Relization of Crystal Bases for Special Linear Lie Algebras

We give a new realization of crystal bases for finite dimensional irreducible modules over special linear Lie algebras using the monomials introduced by H. Nakajima. We also discuss the connection between this monomial realization and the tableau realization given by Kashiwara and Nakashima.Comment: 15 page

The economic explainability of machine learning and standard econometric models-an application to the U.S. mortgage default risk

This study aims to bridge the gap between two perspectives of explainability−machine learning and engineering, and economics and standard econometrics−by applying three marginal measurements. The existing real estate literature has primarily used econometric models to analyze the factors that affect the default risk of mortgage loans. However, in this study, we estimate a default risk model using a machine learning-based approach with the help of a U.S. securitized mortgage loan database. Moreover, we compare the economic explainability of the models by calculating the marginal effect and marginal importance of individual risk factors using both econometric and machine learning approaches. Machine learning-based models are quite effective in terms of predictive power; however, the general perception is that they do not efficiently explain the causal relationships within them. This study utilizes the concepts of marginal effects and marginal importance to compare the explanatory power of individual input variables in various models. This can simultaneously help improve the explainability of machine learning techniques and enhance the performance of standard econometric methods

Population Dynamics in Diffusive Coupled Insect Population

A variety of ecological models exhibit chaotic dynamics because of nonlinearities in population growth and interactions. Here, we will study the LPA model (beetle Tribolium). The LPA model is known to exhibit chaos. In this project, we investigate two things which are the effect of noise constant and the effect of diffusion combined with the LPA model. The effect of noise is not only to change the dynamics of total population density but also to blur the bifurcation diagram. Numerical simulations of the model have shown that diffusion can drive the total population of insects into complex patterns of variability in time. We will compare these simulations with simulations without diffusion. And we conclude that the diffusion coefficient is a bifurcation parameter and that there exist parameter regions with chaotic behavior and periodic solutions. This study demonstrates how diffusion term can be used to influence the chaotic dynamics of an insect population

Young Wall Realization of Crystal Bases for Classical Lie Algebras

In this paper, we give a new realization of crystal bases for finite dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight vectors.Comment: 27page