25 citations · 135 across the 12 of their papers we have counts for
14 papers
QMC integration based on arbitrary (t,m,s)-nets yields optimal convergence rates on several scales of function spaces
Michael Gnewuch, Josef Dick, Lev Markhasin +1
We study the integration problem over the -dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions who…
DPHMs: Diffusion Parametric Head Models for Depth-based Tracking
Jiapeng Tang, Angela Dai, Yinyu Nie +3
We introduce Diffusion Parametric Head Models (DPHMs), a generative model that enables robust volumetric head reconstruction and tracking from monocular depth sequences. While rece…
DiffuScene: Denoising Diffusion Models for Generative Indoor Scene Synthesis
Jiapeng Tang, Yinyu Nie, Lev Markhasin +3
We present DiffuScene for indoor 3D scene synthesis based on a novel scene configuration denoising diffusion model. It generates 3D instance properties stored in an unordered objec…
Neural Shape Deformation Priors
Jiapeng Tang, Lev Markhasin, Bi Wang +2
We present Neural Shape Deformation Priors, a novel method for shape manipulation that predicts mesh deformations of non-rigid objects from user-provided handle movements. State-of…
TAFIM: Targeted Adversarial Attacks against Facial Image Manipulations
Shivangi Aneja, Lev Markhasin, Matthias Niessner
Face manipulation methods can be misused to affect an individual's privacy or to spread disinformation. To this end, we introduce a novel data-driven approach that produces image-s…
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness
Josef Dick, Aicke Hinrichs, Lev Markhasin +1
The discrepancy function measures the deviation of the empirical distribution of a point set in from the uniform distribution. In this paper, we study the classical discr…
Optimal -discrepancy bounds for second order digital sequences
Josef Dick, Aicke Hinrichs, Lev Markhasin +1
The -discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all a lower bound for the $L…
Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions
Aicke Hinrichs, Lev Markhasin, Jens Oettershagen +1
We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces with dominating mixed smoothnes…
BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension
Dmitriy Bilyk, Lev Markhasin
In the current paper we obtain discrepancy estimates in exponential Orlicz and BMO spaces in arbitrary dimension . In particular, we use dyadic harmonic analysis to prove…
L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets
Lev Markhasin
Dick proved that all order digital nets satisfy optimal upper bounds of the -discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prov…
Discrepancy and integration in function spaces with dominating mixed smoothness
Lev Markhasin
Optimal lower bounds for discrepancy in Besov spaces with dominating mixed smoothness are known from the work of Triebel. Hinrichs proved upper bounds in the plane. In this work we…
Quasi-Monte Carlo methods for integration of functions with dominating mixed smoothness in arbitrary dimension
Lev Markhasin
In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible -norm of the discrepancy function. We consider the discrepanc…
Discrepancy of generalized Hammersley type point sets in Besov spaces of dominating mixed smoothness
Lev Markhasin
The symmetrized Hammersley point set is known to achieve the best possible rate for the -norm of the discrepancy function. Also lower bounds for the norm in Besov spaces of do…
On lower bounds for the L_2-discrepancy
Aicke Hinrichs, Lev Markhasin
The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our m…