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The computational complexity of a problem arising in the context of sparse optimization is considered, namely, the projection onto the set of $k$-cosparse vectors w.r.t. some given matrix $\Omeg$. It is shown that this projection problem is…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…
Over the past decade, cryogenic electron microscopy (cryo-EM) has emerged as a primary method for determining near-native, near-atomic resolution 3D structures of biological macromolecules. In order to meet increasing demand for cryo-EM,…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
Solving inverse problems in natural sciences often requires a search pro- cess to find explanatory models that match collected field data. Inverse problems are often under-determined meaning that there are many poten- tial explanatory…
In single-molecule super-resolution microscopy, engineered point-spread functions (PSFs) are designed to efficiently encode new molecular properties, such as 3D orientation, into complex spatial features captured by a camera. To fully…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
We study a class of orbit recovery problems in which we observe independent copies of an unknown element of $\mathbb{R}^p$, each linearly acted upon by a random element of some group (such as $\mathbb{Z}/p$ or $\mathrm{SO}(3)$) and then…
Constructing of molecular structural models from Cryo-Electron Microscopy (Cryo-EM) density volumes is the critical last step of structure determination by Cryo-EM technologies. Methods have evolved from manual construction by structural…
We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint…
Alignment and orientation of molecules by intense, ultrashort laser fields are crucial for a variety of applications in physics and chemistry. These include control of high harmonics generation, molecular orbitals tomography, control of…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
We consider the problem of estimating an unbiased and reference-free ab-inito model for non-symmetric molecules from images generated by single-particle cryo-electron microscopy. The proposed algorithm finds the globally optimal assignment…
We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…
We consider a class of optimization problems defined by a system of linear equations with min and max operators. This class of optimization problems has been studied under restrictive conditions, such as, (C1) the halting or stability…
This paper presents high-order (HO) electromagnetic modeling of plasmonic nanostructures based on the Locally Corrected Nystrom (LCN) method. Advanced nanophotonic and nanoplasmonic structures involve electrically large electromagnetic…
There is a clear need for developments in characterisation techniques that provide detailed information about structure-function relationships in biology. Using electron microscopy to achieve high resolution while maintaining a broad field…