(1.1) { Γ(α)Ψ(α,α−γ+1;ξ) }−1 exp(−ξv)v(1+v), v > 0, (1.2) respectively, where α > 0, β > 0, ξ > 0, −∞ < γ,λ < ∞, 1F1, and Ψ are confluent hypergeometric functions. These distributions are extensions of Gamma and Beta distributions, and for α < 1 (and certain values of λ and γ) yield bimodal distributions on finite and infinite ranges, respectively. These distributions are used (i) in the Bayesi...

It is becoming increasingly important to learn from a partially-observed random matrix and predict its missing elements. We assume that the entire matrix is a single sample drawn from a matrix-variate t distribution and suggest a matrixvariate tmodel (MVTM) to predict those missing elements. We show that MVTM generalizes a range of known probabilistic models, and automatically performs model se...

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-ord...

A grid polygon is a polygon whose vertices are points of a grid. We define an injective map between permutations of length n and a subset of grid polygons on n vertices, which we call consecutive-minima polygons. By the kernel method, we enumerate sets of permutations whose consecutive-minima polygons satisfy specific geometric conditions. We deal with 2-variate and 3-variate generating functions.

Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one is able to recover the graphs and covariance matrices with a single random m...

We refer to human-robot relationships as Lovotics. In this paper a design process for Lovotics is presented. In order to invoke these relationships, technological solutions can only take us so far. Design played an important role in order to engage users to explore the possibilities of bi-directional, human-robot love. We conducted a user-centric study in order to understand these factors and i...

Our previous human fMRI study found brain activations correlated with tactile stickiness perception using the uni-variate general linear model (GLM) (Yeon et al., 2017). Here, we conducted an in-depth investigation on neural correlates of sticky sensations by employing a multivoxel pattern analysis (MVPA) on the same dataset. In particular, we statistically compared multi-variate neural activit...

A hitting-set generator (HSG) is a polynomial map $G:\mathbb{F}^k \to \mathbb{F}^n$ such that for all $n$-variate polynomials $C$ of small enough circuit size and degree, if nonzero, then $C\circ G$ nonzero. In this paper, we give new construction an HSG assuming have explicit sufficient hardness. Formally, prove the following over any field characteristic zero: Let $k\in \mathbb{N}$ $\delta ...

In this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric f...

In this paper, we applied the standard Monte Carlo, antithetic variate, and control variates methods to value double barrier knock-in option price. The underlying asset used in calculation of is share ANTM from April 1, 2019 until March 2022. simulated using methods. results showed that all converge exact solution, with variate method be fastest. Standard Carlo has least computational time, fol...