相关论文: Representation theoretic patterns in three dimensi…

Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…

Single particle electron cryomicroscopy (cryo-EM) allows for structures of proteins and protein complexes to be determined from images of non-crystalline specimens. Cryo-EM data analysis requires electron microscope images of randomly…

We present a coherent approach to recurrence and transience, starting from a version of the Riesz decomposition theorem for superharmonic elements. Our approach allows straightforward proofs of some known results, entails new theorems, and…

We presented a new 3D refinement method for Cryo-EM single particle analysis which can improve the resolution of final electron density map in this paper. We proposed to enforce both sparsity and smoothness to improve the regularity of…

We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain $2n \times n$ matrix storing properly-scaled basis vectors for the…

A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…

Cryogenic electron microscopy (cryo-EM) has transformed structural biology by allowing to reconstruct 3D biomolecular structures up to near-atomic resolution. However, the 3D reconstruction process remains challenging, as the 3D structures…

The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Methods as Method of the…

We prove the existence of a new algorithm for 3-sphere recognition based on Groebner basis methods applied to the variety of $\text{\em SL}(2,\C)$-representation of the fundamental group. An essential input is a recent result of the second…

Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal…

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and…

The irreversible emergence of classical behavior from a reduced quantum description via a canonical intrinsic decomposition of the density operator is analyzed. In the intrinsic reference basis (IRB), defined for a fixed physical…

We present a geometry-aware method for heterogeneous single-particle cryogenic electron microscopy (cryo-EM) reconstruction that predicts atomic backbone conformations. To incorporate protein-structure priors, we represent the backbone as a…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

The three-dimensional structure of proteins plays a crucial role in determining their function. Protein structure prediction methods, like AlphaFold, offer rapid access to a protein structure. However, large protein complexes cannot be…

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…

Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…

The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an…

In this paper, we give new proofs of the celebrated Andr\'eka-Resek-Thompson representability results of certain axiomatized cylindric-like algebras. Such representability results provide completeness theorems for variants of first order…