Related papers: Linear combinations of frame generators in systems…

In this paper we present a combinatorial machinery, consisting of a graph tower $\overleftarrow \Gamma$ and vector towers $\overleftarrow v$ on $\overleftarrow \Gamma$, which allows us to efficiently describe all invariant measures $\mu =…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

In 2008, L\'aszl\'o Z\'adori proved that the lattice Sub$(V)$ of all subspaces of a vector space $V$ of finite dimension at least 3 over a finite field $F$ has a 5-element generating set; in other words, Sub$(V)$ is 5-generated. We prove…

Rotational tangle diagrams have been proven to be extremely important in the study of quantum invariants, as they provide a natural passage between topology and quantum algebra. In this paper, we give a detailed description of several…

A L\'evy process on a *-bialgebra is given by its generator, a conditionally positive hermitian linear functional vanishing at the unit element. A *-algebra homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k…

We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we…

For graded Hilbert spaces $H$ and shift-like commuting tuples $T \in B(H)^n$, we show that each homogeneous joint invariant subspace $M$ of $T$ has finite index and is generated by its wandering subspace. Under suitable conditions on the…

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V^G-modules which occur as submodules of irreducible V-modules by using intertwining operators for…

We prove the equivalence of the frame property and the closedness for a weighted shift-invariant space. We also construct a sequence $\Phi^{2k+1}$ and the sequence of spaces $V^p_\mu(\Phi^{2k+1})$, $k\in{\mathbb{N}}$, on $\mathbb{R},$ with…

We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that ifthetranslates are taken only from a subset of the natural…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully asynchronous application of the elementary cellular automaton 57…

A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…

In this paper we introduce a graph structure, called subspace sum graph $\mathcal{G}(\mathbb{V})$ on a finite dimensional vector space $\mathbb{V}$ where the vertex set is the collection of non-trivial proper subspaces of a vector space and…

It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…

We construct a uniformly discrete, and even sparse, sequence of real numbers $\Lambda=\{\lambda_n\}$ and a function g in $L^2(R)$, such that for every q>2, every function f in $L^2(R)$ can be approximated with arbitrary small error by a…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

In this work, we introduce an unconditional video generative model, InMoDeGAN, targeted to (a) generate high quality videos, as well as to (b) allow for interpretation of the latent space. For the latter, we place emphasis on interpreting…

This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a…