Related papers: Revisiting 2x2 matrix optics: Complex vectors, Fer…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
We have derived a new system of mKdV-type equations which can be related to the affine Lie algebra $A_{5}^{(2)}$. This system of partial differential equations is integrable via the inverse scattering method. It admits a Hamiltonian…
Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix…
End-to-end optimization, which simultaneously optimizes optics and algorithms, has emerged as a powerful data-driven method for computational imaging system design. This method achieves joint optimization through backpropagation by…
Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that…
Gauge fields are special in the sense that they are invariant under gauge transformations and \QTR{em}{``ipso facto''} they lead to problems when we try quantizing them straightforwardly. To circumvent this problem we need to specify a…
In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…
A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional topological order and…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor {\mu} \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients…
It has been recently demonstrated that integrated optics could enhance accuracy, stability, and ease of use of stellar interferometry techniques. The subject of this thesis is the study of an optical component based on singlemode waveguides…
A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row determinants recently introduced by the…
We develop a general gauge invariant Lagrangian construction for half-integer higher spin fields in the AdS space of any dimension. Starting with formulation in terms of auxiliary Fock space we derive the closed nonlinear symmetry algebras…
Integrating conventional optics into compact nanostructured surfaces is the goal of flat optics. Despite the enormous progress of this technology, there are still critical challenges for real world applications due to a limited efficiency…
An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The…
We present an algorithm for holographic shaping of partially coherent light, bridging the gap between traditional coherent and geometric optical approaches. The description of partially coherent light relies on a mode expansion formalism,…
The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \rangle$ which are embeddable into the canonical frame of its Urquhart complex algebra.
We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case…
The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
We use a space-time asymmetric O(a) improved fermion action and fix the asymmetry non-perturbatively to restore the relativistic dispersion relation. We compute spectra and matrix elements of quarkonia and heavy-light mesons and compare…