Compressive nano-FTIR chemical mapping

Nano-Fourier-transform infrared spectroscopy (nano-FTIR) combines infrared spectroscopy with scanning probe microscopy (SPM) techniques and enables spectroscopic imaging of molecular and electronic properties of matter at nanometer spatial resolution. The spectroscopic imaging can be used to derive chemical mappings, i.e., the spatial distribution of concentrations of the species contained in a given sample. However, due to the sequential scanning principle underlying SPM, recording the complete spectrum over a large spatial area leads to long measurement times. Furthermore, the acquired spectrum often contains additional signals from species and lineshape effects that are not explicitly accounted for. A compressive chemical mapping approach is proposed for undersampled nano-FTIR data that utilizes sparsity of these additional signals in the spectral domain. The approach combines a projection technique with standard compressed sensing, followed by a spatially regularized regression. Using real nano-FTIR measurements superimposed by simulated interferograms representing the chemical mapping of the contained species, it is demonstrated that the proposed procedure performs well even in cases in which the simulated interferograms and the sparse additional signals exhibit a strong spectral overlap.

On the squashed seven-sphere operator spectrum

We derive major parts of the eigenvalue spectrum of the operators on the squashed seven-sphere that appear in the compactification of eleven-dimensional supergravity. These spectra determine the mass spectrum of the fields in AdS4 and are important for the corresponding $$ \mathcal{N} $$ N = 1 supermultiplet structure. This work is a continuation of the work in [1] where the complete spectrum of irreducible isometry representations of the fields in AdS4 was derived for this compactification. Some comments are also made concerning the G2 holonomy and its implications on the structure of the operator equations on the squashed seven-sphere.

The construction of a photoabsorption spectrum using the FEFF 9 package: a detailed procedure

A procedure to obtain a photoabsorption spectrum assembled from first-principles calculations made with the FEFF 9 spectroscopy package is presented. The calculation consists of obtaining the absorption cross-section of electromagnetic radiation for each electronic shell of an atom inside a solid; the total value is obtained by the sum of the contributions of all shells. A complete spectrum is shown for metallic copper as an example, covering values from ultraviolet above 10 eV (approximately) to x-rays. The spectrum is compared selectively with values from frequently used tables and with results taken from the literature. The advantages of the FEFF 9 package and its limitations are compared; as well, the preliminary nature of the presented results and the need for convergence studies are highlighted, suggesting future work.

Non-invertible global symmetries and completeness of the spectrum

It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

ETV6/RUNX1 fusion gene and its active role

Recent investigation successfully identified a pre leukemic ETV6/RUNX1-positive clone in the healthy twin of a patient diagnosed with ETV6/RUNXI-positive acute lymphoblastic leukemia (ALL) and also some studies with ETV6/RUNX1 knock in mice showed that the expression of the fusion gene is not sufficient for the invivo induction of ALL. Taken together, these data indicate that ETV6/RUNX1-positive leukemia is .generated through a multi-step mechanism, and that accumulation of additional genetic changes is necessary for the development of overt leukemia. Hence, to understand fully the genetic evolution of this disorder, identification of the complete spectrum of genetic changes that accompany the ETV6/RUNX1 fusion gene is necessary. Moreover, critical patho genetic insights may be gained from studying the correlation pattern of the different copy number changes.

Solitons in fiber Bragg gratings with cubic–quartic dispersive reflectivity having Kerr law of nonlinear refractive index

This paper retrieves soliton solutions to fiber Bragg ratings with dispersive reflectivity where cubic–quartic dispersive effects are considered as opposed to the usual chromatic dispersion. The auxiliary equation approach and an addendum to Kudryashov’s scheme display a complete spectrum of soliton forms to the model that is studied with Kerr effect.

Approximate Atomic Green Functions

In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on classes of virtual excitations, or so-called excitation schemes, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of Jac, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.

Kaluza-Klein fermion mass matrices from exceptional field theory and $$ \mathcal{N} $$ = 1 spectra

Using Exceptional Field Theory, we determine the infinite-dimensional mass matrices for the gravitino and spin-1/2 Kaluza-Klein perturbations above a class of anti-de Sitter solutions of M-theory and massive type IIA string theory with topologically-spherical internal spaces. We then use these mass matrices to compute the spectrum of Kaluza-Klein fermions about some solutions in this class with internal symmetry groups containing SU(3). Combining these results with previously known bosonic sectors of the spectra, we give the complete spectrum about some $$ \mathcal{N} $$ N = 1 and some non-supersymmetric solutions in this class. The complete spectra are shown to enjoy certain generic features.

Asymptotic behaviors of the semigroup of the linearized Landau operator for the very soft and Coulomb potentials

We study the asymptotic behaviors of the semigroup generated by the linearized Landau operator in the case of the very soft potentials and Coulomb potential. Compared with the hard potentials, Maxwellian molecules and moderately soft potentials, there is no spectral gap for the linearized Landau operator with the very soft and Coulomb potentials. By introducing a new decomposition of the linear Landau collision operator $L$ including an accretive operator and a relatively compact operator, we establish the complete spectrum structure for the linearized Landau operator with the very soft and Coulomb potentials and furthermore derive the time decay estimates of the corresponding semigroup in a weighted velocity space.