Related papers: On foundational discretization barriers in STFT ph…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
We define, within the Schroedinger functional scheme (SF), the matrix elements of the twist-2 operators corresponding to the first two moments of non-singlet parton densities. We perform a lattice one-loop calculation that fixes the…
We consider Gabor Riesz sequences generated by a lattice $\Lambda \subset \mathbb{R}^2$ and a window function $g \in L^2(\mathbb{R})$ which is well localized in both time and frequency. When $g$ belongs to the Feichtinger algebra, we prove…
Zero-forcing (ZF) decoder is a commonly used approximation solution of the integer least squares problem which arises in communications and many other applications. Numerically simulations have shown that the LLL reduction can usually…
A phase retrieval technique using a spatial light modulator (SLM) and a phase diffuser for a fast reconstruction of smooth wave fronts is demonstrated experimentally. Diffuse illumination of a smooth test object with the aid of a phase…
We give some new results related to the directional short-time Fourier transform (DSTFT) and extend them on the spaces $\mathcal K_{1}(\mathbb R^{n})$ and $\mathcal K_{1}({\mathbb R})\widehat{\otimes}\mathcal U(\mathbb C^n)$ and their…
Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…
We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…
An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as non-binary belief propagation on associated TGs;…
Let $S$ be the dyadic bi-parameter square function $$Sf(x)^{2} = \sum_{R \in \mathcal{D}} |\langle f, h_{R} \rangle|^{2} \frac{1_{R}(x)}{|R|}.$$ We prove that if $T$ is a bi-parameter martingale transform and $f,g$ are suitable test…
Scattering phase functions (SPFs) derived from resolved scattered-light images of debris discs are widely used to infer dust grain properties, often via parametric forms such as the Henyey-Greenstein (HG) phase function. However, it remains…
Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the…
We show that problems of existence and characterization of wavelets for non-expanding dilations are intimately connected with the geometry of numbers; more specifically, with a bound on the number of lattice points in balls dilated by the…
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…
A non-iterative method is presented to calculate the closest Wannier functions (CWFs) to a given set of localized guiding functions, such as atomic orbitals, hybrid atomic orbitals, and molecular orbitals, based on minimization of a…
Phase retrieval is known to always be unstable when using a frame or continuous frame for an infinite dimensional Hilbert space. We consider a generalization of phase retrieval to the setting of subspaces of $L_2$ which coincides with using…
The weak coupling expansion is applied to the single flavour Schwinger model with Wilson fermions on a symmetric toroidal lattice of finite extent. We develop a new analytic method which permits the expression of the partition function as a…
Let $\Omega$ be a complex lattice which does not have complex multiplication and $\wp=\wp_\Omega$ the Weierstrass $\wp$-function associated to it. Let $D\subseteq\mathbb{C}$ be a disc and $I\subseteq\mathbb{R}$ be a bounded closed interval…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…