Total variation denoising in l1l^1 anisotropy

We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underlying anisotropic total variation functional. We consider a naturally defined class of functions piecewise constant on rectangles (PCR). This class forms a strictly dense subset of the space of functions of bounded variation with an anisotropic norm. The main result shows that if the given noisy image is a PCR function, then solutions to both considered problems also have this property. For PCR data the problem of finding the solution is reduced to a finite algorithm. We discuss some implications of this result, for instance we use it to prove that continuity is preserved by both considered problems.Comment: 34 pages, 9 figure

On the existence of traveling waves in the 3D Boussinesq system

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moir\'{e} minibands of twistronic graphene, one related to direct hybridization of Dirac states, and the other resulting from band folding caused by moir\'{e} superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for non-invasive characterization of the twist, even in hBN-encapsulated structures.Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplemen

Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting material. This is the accepted version of the manuscript (the definitive version appeared in Science), with typographical corrections included her

Energy solutions to one-dimensional singular parabolic problems with BVBV data are viscosity solutions

We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga.Comment: 15 page

A caricature of a singular curvature flow in the plane

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For a class of initial data we are able to study in details the facet formation and interactions and their asymptotic behavior. We notice that our qualitative results may be interpreted with the help of a special composition of multivalued operators

Quantum dynamics and spectroscopy of photodetachment in Cl-...H2O and Cl-...D2O complexes

We have modeled Zero Electron Kinetic Energy (ZEKE) spectra of Cl-…H2O and Cl-…D2O complexes using 3D quantum dynamical simulations on the three low-lying electronic states of the nascent neutral systems. Time-dependent quantum simulations combined with anionic and neutral stationary-state calculations by imaginary time propagation allowed for a detailed interpretation of the spectral features in terms of the underlying dynamics. Because of large differences between the anionic and neutral potential surfaces, the systems are found after electron photodetachment primarily high above the dissociation threshold. Nevertheless, pronounced long-lived resonances are observed, particularly for the lowest neutral state, reflecting the fact that a significant portion of the excess energy is initially deposited into nondissociative modes, that is, to (hindered) water rotation. These resonances form bands corresponding to water rotational states with a fine structure due to intermolecular stretch progressions. Comparison is made to experimental zero electron kinetic energy (ZEKE) spectra of the I-…H2O complex, where analogous anharmonic vibrational progressions have been observed

Smart operational load monitoring using decision trees and artificial neural networks: a comparative study

Operational Load Monitoring is an industrial process that allows to predict the remaining in-service life of a mechanical structure under variable loads. Data from sensors embedded or mounted on the structure is acquired and allows to estimate the number and amplitude of load cycles that the structure has withstood so far in its working environment. This process is especially important in the aerospace industry where mechanical structures of an aircraft are monitored in order to maximize their operating lifetime. Smart Operational Load Monitoring means implementation of artificial intelligence techniques to the process in order to make predictions based on measurements from reduced number of sensors. In this paper a composite lightweight structure of typical geometry used in aircraft structures is taken as an example for Smart Operational Load Monitoring. The predictions are made from measurements from six strain gauges mounted to the structure, using carefully prepared artificial intelligence-based models. Efficiency of the models is compared, in terms of their prediction accuracies and computational complexities.National Agency for Academic Exchange of PolandSilesian University of Technology. Faculty of Mechanical Engineerin

Remote participation during glycosylation reactions of galactose building blocks: Direct evidence from cryogenic vibrational spectroscopy

The stereoselective formation of 1,2‐cis‐glycosidic bonds is challenging. However, 1,2‐cis‐selectivity can be induced by remote participation of C4 or C6 ester groups. Reactions involving remote participation are believed to proceed via a key ionic intermediate, the glycosyl cation. Although mechanistic pathways were postulated many years ago, the structure of the reaction intermediates remained elusive owing to their short‐lived nature. Herein, we unravel the structure of glycosyl cations involved in remote participation reactions via cryogenic vibrational spectroscopy and first principles theory. Acetyl groups at C4 ensure α‐selective galactosylations by forming a covalent bond to the anomeric carbon in dioxolenium‐type ions. Unexpectedly, also benzyl ether protecting groups can engage in remote participation and promote the stereoselective formation of 1,2‐cis‐glycosidic bonds