相关论文: Simplification Rules for Birdtrack Operators

We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set for a…

We show that similarity (or equivalent) transformations enable one to construct non-Hermitian operators with real spectrum. In this way we can also prove and generalize the results obtained by other authors by means of a gauge-like…

The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light…

In this paper, we give some results concerning atomic decompositions for operators on reproducing kernel Hilbert spaces, using frame theory techniques. We provide also generalizations for atomic decompositions of some theorems for…

Previous works have attempted to improve tracking efficiency through lightweight architecture design or knowledge distillation from teacher models to compact student trackers. However, these solutions often sacrifice accuracy for speed to a…

We present a straightforward source-to-source transformation that introduces justifications for user-defined constraints into the CHR programming language. Then a scheme of two rules suffices to allow for logical retraction (deletion,…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a…

In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…

We consider generalizations of the Sylvester matrix equation, consisting of the sum of a Sylvester operator and a linear operator $\Pi$ with a particular structure. More precisely, the commutator of the matrix coefficients of the operator…

It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of…

In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability,…

Model reduction simplifies complex dynamical systems while preserving essential properties. This paper revisits a recently proposed system-theoretic framework for least squares moment matching. It interprets least squares model reduction in…

We redefine the transition function of elementary cellular automata (ECA) in terms of discrete operators. The operator representation provides a clear hint about the way systems behave both at the local and the global scale. We show that…

We develop a simple formalism of biased tracers that we dub $\mathit{Monkey\ bias}$. In this formalism, a biased tracer field is constructed directly in terms of the linear matter fluctuation field and the set of derivative operators acting…

In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…