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A probabilistic clustering algorithm is proposed for the analysis of forensic DNA mixtures in which individual cells are isolated and short tandem repeats are amplified using the polymerase chain reaction to generate single cell…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult…
Structural dynamics of macromolecules is critical to their structural-function relationship. Cryogenic electron microscopy (CryoEM) provides snapshots of vitrified protein at different compositional and conformational states, and the…
A practical method utilising three-dimensional image pattern matching is proposed which, in principle, is capable of unambiguous determination of the types and positions of atoms in small molecules from defocus series collected at only a…
Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (STED) scanning microscopy that…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
The sensitivity of imaging spectroscopy to haemoglobin derivatives makes it a promising tool for detecting blood. However, due to complexity and high dimensionality of hyperspectral images, the development of hyperspectral blood detection…
The advent of X-ray Free Electron Lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is…
Spectroscopic techniques are essential tools for determining the structure of molecules. Different spectroscopic techniques, such as Nuclear magnetic resonance (NMR), Infrared spectroscopy, and Mass Spectrometry, provide insight into the…
Analyzing microscopy images to extract biological object properties (e.g., their morphological organization, temporal dynamics, and population density) is fundamental to various biomedical research. Yet conducting this manually is costly…
Revealing the structure of complex biological macromolecules, such as proteins, is an essential step for understanding the chemical mechanisms that determine the diversity of their functions. Synchrotron based x-ray crystallography and…
Many living and non-living complex systems can be modeled and understood as collective systems made of heterogeneous components that self-organize and generate nontrivial morphological structures and behaviors. This chapter presents a brief…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
We consider the problem of recovering the three-dimensional atomic structure of a flexible macromolecule from a heterogeneous cryo-EM dataset. The dataset contains noisy tomographic projections of the electrostatic potential of the…
Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Remarkably, analogous high-dimensional, highly-interconnected computational architectures also…
The short pulses of X-ray free electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. The particles are injected into the beam in random orientations and they should be…
The Discrete Morse Theory of Forman appeared to be useful for providing filtration-preserving reductions of complexes in the study of persistent homology. So far, the algorithms computing discrete Morse matchings have only been used for…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…