Preparation First, based on the definitions of A t , Y t , ˜ Z t and Z t , we can write g t = G(s t , r t , X t) = p −1 st p −1 rt (I − X t X ⊤ t)(E st ⊙ A)(E ·rt ⊙ X) = (I − X t X ⊤ t)A t Y t. Then from (6), we have X t+1 = X t + α t g t W t − α 2 t 2 X t g ⊤ t g t W t. Since W t = (I + α 2 t 4 g ⊤ t g t) −1 = I − α 2 t 4 g ⊤ t g t + O(α 4 t), we get X t+1 = X t + α t A t Y t − α t X t X ⊤ t A...

1 Data Sources • Amazon abbreviates the AmazonBinary dataset in Chen’s collection. • Iris is from the UCI machine learning repository . • Votes is from the UCI machine learning repository . • ORL is from the Database of Faces of AT&T. • PIE is from CMU/VASC Image Database. • YaleB is from the Extended Yale Face Database B. • COIL20 is from Columbia University Image Library. • Isolet is from the...

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players’ actions. The players communicate over a strongly connected digraph to send/receive the estimates of the other players’ actions to/from the other local players according to a gossip communication protocol. Due to asymmetric infor...

Standard credit risk models rely on a doubly stochastic structure. Conditional on the evolution of common factors, defaults are independent. Recently, tests by Das, Duffie, Kapadia and Saita (2007) have cast doubt on the empirical validity of this assumption. We modify their estimation approach in two ways. First, we model intra-month patterns in observed defaults. Second, we estimate default i...

Establishing correspondence between features in two images of the same scene taken from different viewing angles is a challenging problem in image processing and computer vision. However, its solution is an important step in many applications like wide baseline stereo, 3D model alignment, creation of panoramic views etc.In this paper, we propose a technique for registration of two images of a f...

A formula for Glynn’s hyperdeterminant detp (p prime) of a square matrix shows that the number of ways to decompose any integral doubly stochastic matrix with row and column sums p− 1 into p− 1 permutation matrices with even product, minus the number of ways with odd product, is 1 (mod p). It follows that the number of even Latin squares of order p− 1 is not equal to the number of odd Latin squ...

where the first factor is a symmetric algebra and the second one is a group algebra. The affine algebra ĝ contains a Heisenberg algebra ĥ. One can define the so-called vertex operators X(α, z) associated to α ∈ Q acting on V essentially using the Heisenberg algebra ĥ. The representation of ĝ on V is then obtained from the action of the Heisenberg algebra ĥ and the vertex operators X(α, z) assoc...

The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation φ of Hn. Their φ-spherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet are always to be a Gelfand triple. Furthermore we study the rela...