相关论文: A certified classification of first-order controll…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control…

A new method for absolute polarimetric calibration of large telescopes is presented. The proposed method is highly accurate and is based on the calibration of a small sub-aperture, which is then extended to the full system by means of…

We classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…

The capability of the adaptive optics to correct for the segmentation error is analyzed in terms of the residual wavefront RMS and the power spectral density of the phase. The analytical model and the end-to-end simulation give…

We describe a practical implementation of the anamorphically curved detector concept. In order to demonstrate its advantages, a telescope lab prototype was developed, built, and tested. It is based on a 4-mirror all-spherical unobscured…

We provide the set of filters (saturated submonoids) in a commutative monoid with a topology (like the spectrum of a ring) and study the resulting spaces.

This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider…

The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…

The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height…

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…

This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…

A general framework for the description of the physical properties of matter by a canonical reduction procedure of tensors is presented; besides geometrical symmetries, this paper emphasizes the role of intrinsic symmetries which are due…

In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…

Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are crucial technologies in the field of medical imaging. Score-based models have proven to be effective in addressing different inverse problems encountered in CT and MRI, such…

In this work we study three topologies defined over the same set: the hedgehog. As the name suggests, the hedgehog can be described as a set of spines identified at a single point. Among others, we give a proof of the Kowalsky hedgehog…

A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…

The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or…