Shotgun reconstruction in the hypercube

Mossel and Ross raised the question of when a random coloring of a graph can be reconstructed from local information, namely, the colorings (with multiplicity) of balls of given radius. In this article, we are concerned with random 2-colorings of the vertices of the -dimensional hypercube, or equivalently random Boolean functions. In the worst case, balls of diameter are required to reconstruct. However, the situation for random colorings is dramatically different: we show that almost every 2-coloring can be reconstructed from the multiset of colorings of balls of radius 2. Furthermore, we show that for , almost every -coloring can be reconstructed from the multiset of colorings of 1-balls.     

The COVID-19 pandemic: model-based evaluation of non-pharmaceutical interventions and prognoses

For the electrically actuated microbeam subjected to a combination of DC and AC voltage loadings, we studied the nonlinear dynamical responses and internal resonance analytically. The flexible boundary condition is considered. The modal interaction due to three-to-one internal resonance between the first and second modes is highlighted. The method of multiple scales is employed to get the modulation equation, which describes the amplitude and phases of the involving modes. Then, the equilibrium solutions of the modulation equation are calculated and their stability is examined. The frequency and force response curves reflecting the primary resonance (the first mode) are presented. We find that the first and second modes in the proposed model are coupled, and hence the energy transfer can occur between the involving modes. Moreover, it is found that the response of the system may encounter Hopf bifurcation for some specific parameters. As for simulation, the Galerkin scheme is applied to verify the analytical results in terms of time history, phase-plane portrait, Fourier spectrum, and Poincare section. The simulation results are in good agreement with the analytical ones.     

A Discussion of Probability Functions and Constraints from a Variational Perspective

Set-Valued and Variational Analysis - Probability constraints are a popular modelling mechanism in applications. They help to model feasible decisions when the latter are taken prior to observing...     

Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

Journal of Statistical Physics - We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these...     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Nanoweb Surface-Mounted Metal–Organic Framework Films with Tunable Amounts of Acid Sites as Tailored Catalysts

Metal–organic frameworks (MOFs) are a promising class of materials for many applications, due to their high chemical tunability and superb porosity. By growing MOFs as (thin-)films, additional properties and potential applications become available. Here, copper (II) 1,3,5-benzenetricarboxylate (Cu-BTC) metal–organic framework (MOF) thin-films are reported, which were synthesized by spin-coating, resulting in “nanowebs”, that is, fiber-like structures. These surface-mounted MOFs (SURMOFs) were studied by using photoinduced force microscopy (PiFM) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). The optimal concentration of precursors (10 mm ) was determined that resulted in chemically homogeneous, pure nanowebs. Furthermore, the morphology and (un)coordinated Cu sites in the web were tuned by varying the rotation speed of the spin-coating process. X-ray diffraction (XRD) analysis showed that rotation speeds ≥2000 rpm (with precursors in a water/ethanol solution) generate the catena-triaqua-μ-(1,3,5-benzenetricarboxylate)-copper(II), or Cu(BTC)(H₂O)₃ coordination polymer. X-ray photoelectron spectroscopy (XPS) highlighted the strong decrease in number of (defective) Cu⁺ sites, as the nanowebs mainly consist of coordinated Cu²⁺ Lewis acid sites (LAS) and organic linker–linker, for example, hydrogen-bonding, interactions. Finally, the Lewis-acidic character of the Cu sites is illustrated by testing the films as catalysts in the isomerization of α-pinene oxide. The higher number of LAS (≥3000 rpm), result in higher campholenic aldehyde selectivity reaching up to 87.7 %. Furthermore, the strength of a combined micro- and spectroscopic approach in understanding the nature of MOF thin-films in a spatially resolved manner is highlighted.     

Supramolecular Recognition Influences Magnetism in [X@HVIV8VV14O54]6− Self‐Assemblies with Symmetry‐Breaking Guest Anions

Mixed‐valence polyoxovanadates(IV/V) have emerged as one of the most intricate class of supramolecular all‐inorganic host species, able to encapsulate a wide variety of smaller guest templates during their self‐assembly formation process. As showcased herein, the incorporation of guests, though governed solely by ultra‐weak electrostatic and van der Waals interactions, can cause drastic effects on the electronic and magnetic characteristics of the shell complex of the polyoxovanadate. We address the question of methodology for the magnetochemical analysis of virtually isostructural {V^IV/V₂₂O₅₄}‐type polyoxoanions of D_2d symmetry enclosing diamagnetic VO₂F₂^? (C_2v), SCN^? (C_∞v), or ClO₄^? (T_d) template anions. These induce different polarization effects related to differences in their geometric structures, symmetry, ion radii, and valence shells, eventually resulting in a supramolecular modulation of magnetic exchange between the V(3d) electrons that are partly delocalized over the {V₂₂O₅₄} shells. We also include the synthesis and characterization of the novel [V^VO₂F₂@HV^IV₈V^V₁₄O₅₄]^6? system that comprises the rarely encountered discrete difluorovanadate anion as a quasi‐isolated guest species.