We use the method of interlacing families polynomials to derive a simple proof Bourgain and Tzafriri’s Restricted Invertibility Principle, then sharpen result in two ways. show that stable rank can be replaced by Schatten 4-norm tighter bounds hold when number columns matrix under consideration does not greatly exceed its rows. Our are derived from an analysis smallest zeros Jacobi associated L...

Much of the success fingerprint recognition is attributed to minutiae-based representation. It was believed that minutiae templates could not be inverted obtain a high fidelity image, but this assumption has been shown false. The deep learning resulted in alternative representations (embeddings), hope they might offer better accuracy as well non-invertibility network-based templates. We evaluat...

Abstract We define a bicomplex whose Euler characteristic is the idempotented version of ribbon element quantum s l (2). show that properties this descend to centrality, invertibility, and symmetries after decategorification.

The discrete wavelet transform (DWT) is extended to functions on the discrete circle to create a fast and complete discrete periodic wavelet transform (DPWT) for bounded periodic sequences. This extension also solves the problem of non-invertibility that arises in the application of the DWT to finite-dimensional sequences and provides the proper theoretical setting for previous incomplete solut...

We determine optimal L-properties for the solutions of the general nonlinear elliptic system in the plane of the form fz = H(z, fz), h ∈ L(C), where H is a measurable function satisfying |H(z,w1) − H(z,w2)| ≤ k|w1 − w2| and k is a constant k < 1. We also establish the precise invertibility and spectral properties in L(C) for the operators I − T μ, I − μT, and T − μ, where T is the Beurling tran...

Abstract: Let (W,H,μ) be the classical Wiener space. Assume that U = IW + u is an adapted perturbation of identity, i.e., u : W → H is adapted to the canonical filtration ofW . We give some sufficient analytic conditions on u which imply the invertibility of the map U . In particular it is shown that if u ∈ IDp,1(H) is adapted and if exp( 2‖∇u‖2 − δu) ∈ Lq(μ), where p−1 + q−1 = 1, then IW + u i...