Forgiveness in the Criminal Justice System: If it Belongs, then Why is it so Hard to Find?

This essay advocates the role of forgiveness within the criminal justice system, particularly from a prosecutor\u27s perspective, and discusses common impediments to its increased presence and the leadership needed to allow it to develop within the system

Equivariant differential characters and symplectic reduction

We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction

Variational Data Assimilation via Sparse Regularization

This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable of interest exhibits sparsity in the real or transformed domain. We show that in the presence of sparsity, the $\ell_{1}$-norm regularization produces more accurate and stable solutions than the classic data assimilation methods. To motivate further developments of the proposed methodology, assimilation experiments are conducted in the wavelet and spectral domain using the linear advection-diffusion equation

The symplectic Deligne-Mumford stack associated to a stacky polytope

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic

Dynamical phenomena near a homo- or heteroclinic connection involving saddle-foci in a Hamiltonian system

The main features of the orbit behavior for a Hamiltonian system in a neighborhood of a homoclinic orbit to a saddle-focus equilibrium or of a contour made up of two saddle-foci and two heteroclinic orbits to them are presented. These features includes description of hyperbolic subsets and main bifurcations when varying a value of the Hamiltonian and parameters. The proofs of results about bifurcations are given