Optimization of STEM-HAADF Electron Tomography Reconstructions by Parameter Selection in Compressed Sensing Total Variation Minimization-Based Algorithms

A novel procedure to optimize the 3D morphological characterization of nanomaterials by means of high angle annular dark field scanning-transmission electron tomography is reported and is successfully applied to the analysis of a metal- and halogen-free ordered mesoporous carbon material. The new method is based on a selection of the two parameters (μ and β) which are key in the reconstruction of tomographic series by means of total variation minimization (TVM). The parameter-selected TVM reconstructions obtained using this approach clearly reveal the porous structure of the carbon-based material as consisting of a network of parallel, straight channels of ≈6 nm diameter ordered in a honeycomb-type arrangement. Such an unusual structure cannot be retrieved from a TVM 3D reconstruction using default reconstruction values. Moreover, segmentation and further quantification of the optimized 3D tomographic reconstruction provide values for different textural parameters, such as pore size distribution and specific pore volume that match very closely with those determined by macroscopic physisorption techniques. The approach developed can be extended to other reconstruction models in which the final result is influenced by parameter choice.     

The Impact of Research Culture on Mental Health & Diversity in STEM

The onset of COVID-19, coupled with the finer lens placed on systemic racial disparities within our society, has resulted in increased discussions around mental health. Despite this, mental health struggles in research are still often viewed as individual weaknesses and not the result of a larger dysfunctional research culture. Mental health interventions in the science, technology, engineering, and mathematics (STEM) academic community often focus on what individuals can do to improve their mental health instead of focusing on improving the research environment. In this paper, we present four aspects of research that may heavily impact mental health based on our experiences as research scientists: bullying and harassment; precarity of contracts; diversity, inclusion, and accessibility; and the competitive research landscape. Based on these aspects, we propose systemic changes that institutions must adopt to ensure their research culture is supportive and allows everyone to thrive.     

Word problems and ceers

This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non-periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non-commutative and non-Boolean c.e. ring.     

Nonclassical Recrystallization

Applications in the fields of materials science and nanotechnology increasingly demand monodisperse nanoparticles in size and shape. Up to now, no general purification procedure exists to thoroughly narrow the size and shape distributions of nanoparticles. Here, we show by analytical ultracentrifugation (AUC) as an absolute and quantitative high-resolution method that multiple recrystallizations of nanocrystals to mesocrystals is a very efficient tool to generate nanocrystals with an excellent and so-far unsurpassed size-distribution (PDI_c=1.0001) and shape. Similar to the crystallization of molecular building blocks, nonclassical recrystallization removes “colloidal” impurities (i.e., nanoparticles, which are different in shape and size from the majority) by assembling them into a mesocrystal. In the case of nanocrystals, this assembly can be size- and shape-selective, since mesocrystals show both long-range packing ordering and preferable crystallographic orientation of nanocrystals. Besides the generation of highly monodisperse nanoparticles, these findings provide highly relevant insights into the crystallization of mesocrystals.     

Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.