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Homogenization in terms of multiscale limits transforms a multiscale problem with $n+1$ asymptotically separated microscales posed on a physical domain $D \subset \mathbb{R}^d$ into a one-scale problem posed on a product domain of dimension…
The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
Multimodal representations that enable cross-modal retrieval are widely used. However, these often lack interpretability making it difficult to explain the retrieved results. Solutions such as learning sparse disentangled representations…
Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…
We introduce a novel framework for implementing error-correction in constrained systems. The main idea of our scheme, called Quantized-Constraint Concatenation (QCC), is to employ a process of embedding the codewords of an error-correcting…
Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
The Elvis problem has been studied in [2], which proves existence of solutions. However, their computation in the non-smooth case remains unsolved. A bisection method is proposed to solve the Elvis problem in two space dimensions for…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
In this paper, we investigate a trade-off between the number of radar observations (or measurements) and their resolution in the context of radar range estimation. To this end, we introduce a novel estimation scheme that can deal with…
Multipartite entanglement underpins quantum technologies but its study is limited by the lack of universal measures, unified frameworks, and the intractability of convex-roof extensions. We establish an axiomatic framework and introduce the…
This work is concerned with the problem of recovering high-dimensional signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of low-complexity from a small number of quantized measurements. We propose to estimate the signals…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
This paper presents a novel method for rare event detection from an image pair with class-imbalanced datasets. A straightforward approach for event detection tasks is to train a detection network from a large-scale dataset in an end-to-end…
Recent advances in diffusion models have enabled the creation of deceptively real images, posing significant security risks when misused. In this study, we empirically show that different timesteps of DDIM inversion reveal varying subtle…
The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…