Related papers: The Jacobian as a measure of planar dose congruenc…
This work studies the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian…
We introduce a weak notion of $2\times 2$-minors of gradients of a suitable subclass of $BV$ functions. In the case of maps in $BV(\mathbb{R}^2;\mathbb{R}^2)$ such a notion extends the standard definition of Jacobian determinant to…
We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler-DeWitt supermetric for this field, the first one being based on its algebraic decomposition, the other inspired by…
The paper deals with the distribution of singular values of the input-output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent rectangular…
Most conventional risk analysis methods rely on a single best estimate of exposure per person which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the…
We establish some exact asymptotic results for a matching problem with respect to a family of beta distributions. Let $X_1, \ldots, X_n$ be independent random variables with common distribution the symmetric Jacobi measure $d\mu (x) = C_d…
This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective…
We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit $n$-dimensional cube onto itself, whose Jacobian is equal to $-1$ a.e. Moreover we prove that our homeomorphism can…
In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the…
Some textbooks and reports claim that the Jacobian which arises in the discussion of the Faddeev-Popov method to quantize non-Abelian gauge theories and which is given by the derivative of the gauge fixing conditions over the gauge group…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…
In this paper universality limits are studied in connection with measures which exhibit power-type singular behavior somewhere in their support. We extend the results of Lubinsky for Jacobi measures supported on $ [-1,1] $ to generalized…
Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means are…
We present a comprehensive treatment of relative oscillation theory for finite Jacobi matrices. We show that the difference of the number of eigenvalues of two Jacobi matrices in an interval equals the number of weighted sign-changes of the…
Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface $Y$ is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms on $Y$ quotiented by the torsion-free…
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…
This study presents a proof-of-concept for a novel Bayesian inverse method in a one-dimensional setting, aimed at proton beam therapy treatment verification. Our methodology is predicated on a hypothetical scenario wherein strategically…
We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of ``open abelian varieties'' which satisfies gluing axioms similar to those of Riemann surfaces, and…