Many scientific applications benefit from the accurate and efficient computation of derivatives. Automatically generating these derivative computations from an applications source code offers a competitive alternative to other approaches, such as less accurate numerical approximations or labor-intensive analytical implementations. ADIC2 is a source transformation tool for generating code for co...

Many recent invertible neural architectures are based on coupling block designs where variables divided in two subsets which serve as inputs of an easily (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian very sparse and thus may lack expressiveness. This work presents simple remedy by noting that subdivision (affine) can be repeated recursively ...

We formulate a complete path integral bosonization procedure for any fermionic theory in two dimensions. The classical action of the bosons in the bosonized theory is −i times the logarithm of the Jacobian of a local chiral transformation, with the boson fields as transformation parameters. Three examples, the Schwinger model, the massive Thirring model and massive non-Abelian bosonization, are...

This work investigates the effects of nonrigid transformation model and deformation constraints on the results of deformation-based morphometry (DBM) studies. We evaluate three popular registration algorithms: a B-spline algorithm with several different constraint terms, Thirion's demons algorithm, and a curvature PDE-based algorithm. All algorithms produced virtually identical overlaps of corr...

A special case, called the divergence-free case, of the Jacobian Conjecture in dimension two is proved. This note outlines an argument for a special case of the Jacobian conjecture in dimension two: Suppose F : C → C is a polynomial so that F (0) = 0, F ′(0) = I, det(F ′(z)) = 1, z ∈ C. (1) where I is the identity transformation on C. Write F (x, y) = ( r(x, y) + x s(x, y) + y ) , (x, y) ∈ C wh...

We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Si...

The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. Both forward and inverse kinematics solutions for the TR 4000 educational robot arm are presented. The closed form solution of the inverse kinematics problem is of utmost importance in controlling robotic manipulator. In this paper, a closed form solution to the inverse kinematics...

Jacobian Adaptation (JA) of the acoustic models is an efficient adaptation technique for robust speech recognition. Several improvements for the JA have been proposed in the last years, either to generalize the Jacobian linear transformation for the case of large noise mismatch between training and testing or to extend the adaptation to other degrading factors, like channel distortion and vocal...

Transition from chaotic to quasi-periodic phase in modified Lorenz model is analyzed by performing the contact transformation such that the trajectory in R is projected on R. The relative torsion number and the characteristics of the template are measured using the eigenvector of the Jacobian instead of vectors on moving frame along the closed trajectory. Application to the circulation of a flu...