Let X0 be an unknown M by N matrix. In matrix recovery, one takes n < MN linear measurements y1, . . . , yn of X0, where yi = Tr(ai X0) and each ai is a M by N matrix. For measurement matrices with Gaussian i.i.d entries, it known that if X0 is of low rank, it is recoverable from just a few measurements. A popular approach for matrix recovery is Nuclear Norm Minimization (NNM): solving the conv...

For irreversible diffusion-controlled reactions, it is now widely appreciated that the density decays more slowly than the predictions of mean-field theory in sufficiently low spatial dimension. For two-species annihilation, this behavior is accompanied by the dynamic formation of large-scale spatial heterogeneities in an initially homogeneous system [1]. The contrasting situation where the rea...

a r t i c l e i n f o a b s t r a c t We survey research on the analysis of multiparticipant chat. Multiple research and applied communities (e.g., AI, educational, law enforcement, military) have interest in this topic. After introducing some context, we describe relevant problems and how these have been addressed using AI techniques. We also identify recent research trends and unresolved issu...

As interest in online learning has increased, studies utilizing a social system for the innovation of lecture/learning environments have attracted attention recently. To establish sustainable environment system, prior research investigated strategies to improve and manage presence collaborators (e.g., students, AI facilitators, etc.) an lecture. Nevertheless, negative effect was often neglected...

In this work, we prove the existence of a solution for initial value problem nonlinear fractional differential equation with quadratic perturbations involving Caputo derivative ( cDα0+−ρt cDβ0+)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1&amp;lt;α&amp;lt;2,0&amp;lt;β&amp;lt;α( cD0+α−ρt cD0+β)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1&amp;lt;α&amp;lt;2,0&amp;lt;β&amp;lt;α conditions x0=x(0)f(0,x(0))x0=x(0)f...

Ai = Prismatic joints along the horizontal circular guide Bi = Spherical joints on the moving platform Ci = Prismatic joints on the vertical columns (i = 1,2,3) {F} = Fixed global reference frame {M} = Moving frame α, β, γ = ZYX Euler angles of rotation about the three joint axes of rider. α', β', γ', δ' = ZYXZ’ Euler angles of rotation about the four joint axes of chair on the moving platform ...

This document contains proofs, supplementary details, and supplementary experiments for the paper " Graph Sparsification Approaches for Laplacian Smoothing ". All section numbers, equation numbers, and figure numbers in this supplementary document are preceded by the letter A, to distinguish them from those from the main paper. Part (a). By optimality ofˆθ for problem (5), y − ˆ θ 2 2 + λ ˆ θ T...

Since 1970's AI research has been g e t t i n g more and more a c t i v e in China and c e r t a i n u s e f u l r e s u l t s have been a c h i e v e d . Th is paper i s i n tended t o rev iew b r i e f l y what was and is go ing on in AI f i e l d o f Ch ina .

We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ φp Δu t − 1 q t f t, u t ,Δu t 0, t ∈ {1, . . . , n − 1} subject to the boundary conditions: u 0 0, u n ∑m−2 i 1 aiu ξi , where φp s |s|p−2s, p > 1, ξi ∈ {2, . . . , n − 2} with 1 < ξ1 < · · · < ξm−2 < n − 1 and ai ∈ 0, 1 , 0 < ∑m−2 i 1 ai < 1. Using a new fixed point theorem due to Avery and...

Title of Document: S Y S T E M A T I C I N V E S T I G A T I O N O F QUORUM SENSING IN Escherichia coli JUN LI, Doctor of Philosophy, 2007 Directed By: Professor, William E Bentley, Chemical and Biomolecular Engineering High throughput techniques and advanced mathematical tools have enabled systematic investigations of biological systems with unparalleled precision. Not only molecular interacti...