Mini-Workshop: Bridging Number Theory and Nichols Algebras via Deformations

Nichols algebras are graded Hopf algebra objects in braided tensor categories. They appeared first in a paper by Nichols in 1978 in the search for new examples of Hopf algebras. Rediscovered later several times, they also provide a conceptual explanation of the construction of quantum groups. The aim of the workshop is to review recent developments in the field, initiate collaborations, and discuss new approaches to open problems

On Dykstra's Algorithm with Bregman Projections

We provide quantitative results on the asymptotic behavior of Dykstra's algorithm with Bregman projections, a combination of the well-known Dykstra's algorithm and the method of cyclic Bregman projections, designed to find best approximations and solve the convex feasibility problem in a non-Hilbertian setting. The result we provide arise through the lens of proof mining, a program in mathematical logic which extracts computational information from non-effective proofs. Concretely, we provide a highly uniform and computable rate of metastability of low complexity and, moreover, we also specify general circumstances in which one can obtain full and effective rates of convergence. As a byproduct of our quantitative analysis, we also for the first time establish the strong convergence of Dykstra's method with Bregman projections in infinite dimensional (reflexive) Banach spaces

Emergence of vortex state in the S=1 Kitaev-Heisenberg model with single-ion anisotropy

The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-1 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a ferromagnetic state in the presence of antiferromagnetic Heisenberg interactions, whereas a Néel state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also suggest experimental prospects for observing these novel magnetic states in material realizations

PIEZO1-mediated mechanosensing governs NK cell killing efficiency and infiltration in three-dimensional matrices

Natural killer (NK) cells play a vital role in eliminating tumorigenic cells. Efficient locating and killing of target cells in complex three-dimensional (3D) environments are critical for their functions under physiological conditions. However, the role of mechanosensing in regulating NK cell killing efficiency in physiologically relevant scenarios is poorly understood. Here, we report that the responsiveness of NK cells is regulated by tumor cell stiffness. NK cell killing efficiency in 3D is impaired against softened tumor cells, while it is enhanced against stiffened tumor cells. Notably, the durations required for NK cell killing and detachment are significantly shortened for stiffened tumor cells. Furthermore, we have identified PIEZO1 as the predominantly expressed mechanosensitive ion channel among the examined candidates in NK cells. Perturbation of PIEZO1 abolishes stiffness-dependent NK cell responsiveness, significantly impairs the killing efficiency of NK cells in 3D, and substantially reduces NK cell infiltration into 3D collagen matrices. Conversely, PIEZO1 activation enhances NK killing efficiency as well as infiltration. In conclusion, our findings demonstrate that PIEZO1-mediated mechanosensing is crucial for NK killing functions, highlighting the role of mechanosensing in NK cell killing efficiency under 3D physiological conditions and the influence of environmental physical cues on NK cell functions

Acid Treatments of Ti-Based Metallic Glasses for Improving Corrosion Resistance in Implant Applications

Ti-based bulk metallic glasses are promising materials for metallic bone implants, mainly due to their mechanical biofunctionality. A major drawback is their limited corrosion resistance, with high sensitivity to pitting. Thus, effective surface treatments for these alloys must be developed. This work investigates the electrochemical treatment feasibility of nitric acid (HNO3) solution for two bulk glass-forming alloys. The surface states obtained at different anodic potentials are characterized with electron microscopy and Auger electron spectroscopy. The corrosion behavior of the treated glassy alloys is analyzed via comparison to non-treated states in phosphate-buffered saline solution (PBS) at 37 °C. For the glassy Ti47Zr7.5Cu38Fe2.5Sn2Si1Ag2 alloy, the pre-treatment causes pseudo-dealloying, with a transformation from naturally passivated surfaces to Ti- and Zr-oxide nanoporous layers and Cu-species removal from the near-surface regions. This results in effective suppression of chloride-induced pitting in PBS. The glassy Ti40Zr10Cu34Pd14Sn2 alloy shows lower free corrosion activity in HNO3 and PBS due to Pd stabilizing its strong passivity. However, this alloy undergoes pitting under anodic conditions. Surface pre-treatment results in Cu depletion but causes enrichment of Pd species and non-homogeneous surface oxidation. Therefore, for this glassy alloy, pitting cannot be completely inhibited in PBS. Concluding, anodic treatments in HNO3 are more suitable for Pd-free glassy Ti-based alloys

NaOH protective layer for a stable sodium metal anode in liquid electrolytes

Sodium is known as a soft metal that can easily change its particle morphology. It can form outstretched and rolled fibers with plastic or brittle behavior, and cubes. In Na-batteries, metallic Na anodes demonstrate a high reactivity towards the majority of electrolyte solutions, volume change and a random deposition process from the electrolyte, accompanied by dendrite formation. In order to smooth the electrochemical Na deposition, we propose NaOH as a simple artificial protective layer for sodium, formed by its exposure to ambient conditions for a certain period of time. The formed NaOH layer on top of the metallic sodium suppresses the volume change and dendrite growth on the sodium surface. Additionally, the protected sodium does not change its morphology after a prolonged contact with carbonate-based electrolytes. In symmetric Na-batteries, the NaOH layer increases the lifetime of the electrochemical cell by eight times in comparison to non-protected Na. In the full-cell with a layered sodium oxide cathode, the NaOH-protected sodium anode also leads to a high cycling stability, providing 81 % of the initial cell capacity after 500 cycles with a 1C current rate. In contrast, batteries with a non-protected Na-anode reach only 20 % of their initial capacity under the same conditions. Therefore, the main benefits of the NaOH artificial layer are the chemical compatibility with the carbonate-based electrolytes, the protection of Na metal against reaction with the electrolyte solution, the rapid Na-ion diffusion through the layer and the formation of a mechanical barrier, mitigating Na-dendrite growth. This work presents an easily scalable method to protect sodium without any additional chemicals or a special environment for this reaction

Bibliometrics and Bibliometric Analysis

[no abstract available

Special Issue on Computational Ultrasound Imaging and Applications

[No abstract available

On-Chip Micro Temperature Controllers Based on Freestanding Thermoelectric Nano Films for Low-Power Electronics

Dense and flat freestanding Bi2Te3-based thermoelectric nano films were successfully fabricated by sputtering technology using a newly developed nano graphene oxide membrane as a substrate. On-chip micro temperature controllers were integrated using conventional micro-electromechanical system technology, to achieve energy-efficient temperature control for low-power electronics. The tunable equivalent thermal resistance enables an ultrahigh temperature control capability of 100 K mW−1 and an ultra-fast cooling rate exceeding 2000 K s−1, as well as excellent reliability of up to 1 million cycles

Bioactive glass–ceramics containing fluorapatite, xonotlite, cuspidine and wollastonite form apatite faster than their corresponding glasses

Crystallisation of bioactive glasses has been claimed to negatively affect the ion release from bioactive glasses. Here, we compare ion release and mineralisation in Tris–HCl buffer solution for a series of glass–ceramics and their parent glasses in the system SiO2–CaO–P2O5–CaF2. Time-resolved X-ray diffraction analysis of glass–ceramic degradation, including quantification of crystal fractions by full pattern refinement, show that the glass–ceramics precipitated apatite faster than the corresponding glasses, in agreement with faster ion release from the glass–ceramics. Imaging by transmission electron microscopy and X-ray nano-computed tomography suggest that this accelerated degradation may be caused by the presence of nano-sized channels along the internal crystal/glassy matrix interfaces. In addition, the presence of crystalline fluorapatite in the glass–ceramics facilitated apatite nucleation and crystallisation during immersion. These results suggest that the popular view of bioactive glass crystallisation being a disadvantage for degradation, apatite formation and, subsequently, bioactivity may depend on the actual system study and, thus, has to be reconsidered