1 Text S1: Mathematical basics behind regNet 3 1.1 Network inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Network-based predictions of gene expression levels . . . . . . . . . . . . . . . . 4 1.3 Network propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 Computation of a cohort-specific impact matrix . . . . . . . . . ....

In this project we explore different ways in which we can optimize the computation of training a Tree-structured RNTN, in particular batching techniques in combining many matrix-vector multiplications into matrix-matrix multiplications, and many tensor-vector operations into tensor-matrix operations. We assume that training is performed using mini-batch AdaGrad algorithm, and explore how we can...

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreove...

We investigate the random matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable non-interacting localized electron basis we obtain a sparse random matrix with very long tails which is different from a superimposed random band matrix usually thought to be valid. The number of non-zero off-diagonal matrix elements is shown to decay very ...

This paper covers the problem of Collision Free Path Planning for an autonomous robot and proposes a solution to it through the Back Propagation Neural Network. The solution is transformed into a composition of matrix-multiplication operations, which is a classic example of problems that can be efficiently parallelized. This paper finally proposes a parallel implementation of this matrix-multip...

Analysis of integrated optical cylindrical microresonators involves the coupling between a straight waveguide and a bent waveguide. Our (2D) variant of coupled mode theory is based on analytically represented mode profiles. With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way and solved by numerical integration. Proper manipulation of ...

Prior treatments of space–time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval—in which case there is a nonzero “outage capacity”—or multiple fading intervals—in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In...

We propose a key-frame-based depth propagation method considering movement on the z-axis. First, a homography matrix is obtained through the feature points between points. Through this homography matrix information, a movement of objects or cameras is inferred in the direction of the z axis, thereby creating a depth map that compensates the movement. Then, bilateral filtering is executed to cre...

6 The convolution layer 11 6.1 What is convolution? . . . . . . . . . . . . . . . . . . . . . . . . . 11 6.2 Why to convolve? . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.3 Convolution as matrix product . . . . . . . . . . . . . . . . . . . 15 6.4 The Kronecker product . . . . . . . . . . . . . . . . . . . . . . . 17 6.5 Backward propagation: update the parameters . . . . . . . . ...

The formulation of the extended Kalman lter for a multilayer nonlinear quasi-geostrophic ocean circulation model is discussed. The nonlinearity in the ocean model leads to an approxima-tive equation for error covariance propagation, where the transition matrix is dependent on the state trajectory. This nonlinearity complicates the dynamics of the error covariance propagation, and eeects which a...