Related papers: Generalized canonical purification for density mat…
minimal-lagrangians is a Python program which allows one to specify the field content of an extension of the Standard Model of particle physics and, using this information, to generate the most general renormalizable Lagrangian that…
Cutting out and object and estimate its transparency mask is a key task in many applications. We take on the work on closed-form matting by Levin et al., that is used at the core of many matting techniques, and propose an alternative…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…
High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of…
This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
The structure of the Euler-Lagrange equations for a general Lagrangian theory is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
A strengthened form of Schur's triangularization theorem is given for quaternion matrices with real spectrum (for complex matrices it was given by Littlewood). Littlewood's algorithm for reducing a complex matrix to a canonical form under…
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for…
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion…
It is known that entanglement swapping can be used to realize entanglement purifying. By this way, two particles belong to different non-maximally entangled pairs can be projected probabilisticly to a maximally entangled state or to a less…
We extend Deligne's weight filtration to the integer cohomology of complex analytic spaces (endowed with an equivalence class of compactifications). In general, the weight filtration that we obtain is not part of a mixed Hodge structure.…