In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

We present a map from the travelling salesman problem (TSP), prototypical NP-complete combinatorial optimisation task, to ground state associated with system of many-qudits. Conventionally, TSP is cast into quadratic unconstrained binary (QUBO) problem, that can be solved on an Ising machine. The size corresponding physical system's Hilbert space $2^{N^2}$, where $N$ number cities considered in...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

One of the challenging issues in the domain of C2 in complex and urban terrain is how to assist human combat staff to effectively collaborate and make decisions under multiple contexts, and to help people switch their attentions to the most urgent decision tasks. This paper describes a comprehensive approach that uses RPD-enabled agents to support timely decision-making under multiple contexts....

A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of probability measures. Given a dataset of n samples, EXPoSE needs only O(n) (linear time) to build a model and O(1) (constant time) to make a prediction. In thi...

Representations that can compactly and effectively capture the temporal evolution of semantic content are important to computer vision and machine learning algorithms that operate on multi-variate time-series data. We investigate such representations motivated by the task of human action recognition. Here each data instance is encoded by a multivariate feature (such as via a deep CNN) where act...

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.