Inspired by recent successes of deep learning in computer vision and speech recognition, we propose a novel framework to encode time series data as different types of images, namely, Gramian Angular Fields (GAF) and Markov Transition Fields (MTF). This enables the use of techniques from computer vision for classification. Using a polar coordinate system, GAF images are represented as a Gramian ...

This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system....

In this paper, we describe the use of graph-spectral techniques and their relationship to Riemannian geometry for the purposes of segmentation and grouping. We pose the problem of segmenting a set of tokens as that of partitioning the set of nodes in a graph whose edge weights are given by the geodesic distances between points in a manifold. To do this, we commence by explaining the relationshi...

The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is...

We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class p...

The Fisher information matrix determines how much information a measurement brings about the parameters that index the underlying probability distribution for the measurement. In this paper we assume that the parameters structure the mean value vector in a multivariate normal distribution. The Fisher matrix is. then a Gramian constructed from the sensitivity vectors that characterize the first-...

The theorem is at first surprising, since A has ( n+1 2 ) degrees of freedom, whereas v has only n degrees of freedom (for the explanation see the remark following the proof of Theorem 2). The problem arises from a question in communication theory (see §5), which calls for projections Λv with high packing density. Since both the determinant and minimal norm of a lattice are continuous functions...

Several inequalities for gramian normal operators and for gramian self-adjoint operators in pseudo-Hilbert spaces are presented.

In this paper, we first present the Casorati and grammian determinant solutions to a special two-dimensional lattice by Blaszak and Szum. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the special lattice. Moreover, gram-type pfaffian solutions to the pfaffianized system are proposed. Finally, the bi-directional wronskian solut...

The elementary divisors of the Gram matrices of Specht modules S λ over the symmetric group are determined for two-row partitions and for two-column partitions λ. More precisely, the subquotients of the Jantzen filtration are calculated using Schaper's formula. Moreover, considering a general partition λ of n at a prime p > n − λ 1 , the only possible non trivial composition factor of S λ Fp is...