The Demographic-Wealth model for cliodynamics.

Cliodynamics is a still a relatively new research area with the purpose of investigating and modelling historical processes. One of its first important mathematical models was proposed by Turchin and called "Demographic-Fiscal Model" (DFM). This DFM was one of the first and is one of a few models that link population with state dynamics. In this work, we propose a possible alternative to the classical Turchin DFM, which contributes to further model development and comparison essential for the field of cliodynamics. Our "Demographic-Wealth Model" (DWM) aims to also model link between population and state dynamics but makes different modelling assumptions, particularly about the type of possible taxation. As an important contribution, we employ tools from nonlinear dynamics, e.g., existence theory for periodic orbits as well as analytical and numerical bifurcation analysis, to analyze the DWM. We believe that these tools can also be helpful for many other current and future models in cliodynamics. One particular focus of our analysis is the occurrence of Hopf bifurcations. Therefore, a detailed analysis is developed regarding equilibria and their possible bifurcations. Especially noticeable is the behavior of the so-called coexistence point. While changing different parameters, a variety of Hopf bifurcations occur. In addition, it is indicated, what role Hopf bifurcations may play in the interplay between population and state dynamics. There are critical values of different parameters that yield periodic behavior and limit cycles when exceeded, similar to the "paradox of enrichment" known in ecology. This means that the DWM provides one possible avenue setup to explain in a simple format the existence of secular cycles, which have been observed in historical data. In summary, our model aims to balance simplicity, linking to the underlying processes and the goal to represent secular cycles.

Dispersion-corrected r2SCAN based double-hybrid functionals.

The regularized and restored semi-local meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r2SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create adiabatic-connection-derived global double-hybrid functionals employing spin-opposite-scaled MP2. The 0-DH, CIDH, QIDH, and 0-2 type double-hybrid functionals are assessed as a starting point for further modification. Variants with 50% and 69% Hartree-Fock exchange (HFX) are empirically optimized (Pr2SCAN50 and Pr2SCAN69), and the effect of MP2-regularization (κPr2SCAN50) and range-separated HFX (ωPr2SCAN50) is evaluated. All optimized functionals are combined with the state-of-the-art London dispersion corrections D4 and NL. The resulting functionals are assessed comprehensively for their performance on main-group and metal-organic thermochemistry on 90 different benchmark sets containing 25 800 data points. These include the extensive GMTKN55 database, additional sets for main-group chemistry, and multiple sets for transition-metal complexes, including the ROST61, the MOR41, and the MOBH35 sets. As the main target of this study is the development of a broadly applicable, robust functional with low empiricism, special focus is put on variants with moderate amounts of HFX (50%), which are compared to the so far successful PWPB95-D4 (50% HFX, 20% MP2 correlation) functional. The overall best variant, ωPr2SCAN50-D4, performs well on main-group and metal-organic thermochemistry, followed by Pr2SCAN69-D4 that offers a slight edge for metal-organic thermochemistry and by the low HFX global double-hybrid Pr2SCAN50-D4 that performs robustly across all tested sets. All four optimized functionals, Pr2SCAN69-D4, Pr2SCAN50-D4, κPr2SCAN50-D4, and ωPr2SCAN50-D4, outperform the PWPB95-D4 functional.

Characterization of Fluorescent Dyes Frequently Used for Bioimaging: Photophysics and Photocatalytical Reactions with Proteins.

Derivatives of the rhodamine-based dye 5-TAMRA (5-carboxy-tetramethylrhodamine) and the indocarbocyanine-type Cy3B (cyclized derivative of the cyanine dye Cy3), both representing important fluorophores frequently used for the labeling of biomolecules (proteins, nucleic acids) and bioactive compounds, such as receptor ligands, were photophysically investigated in aqueous solution, i.e., in neat phosphate-buffered saline (PBS) and in PBS supplemented with 1 wt % bovine serum albumin (BSA). The dyes exhibit comparable absorption (λabs,max: 550-569 nm) and emission wavelengths (λem,max: 580-582 nm), and similar S1 lifetimes (2.27-2.75 ns), and their excited state deactivation proceeds mainly via the lowest excited singlet state (triplet quantum yield ca. 1%). However, the probes show marked differences with respect to their fluorescence quantum yield and photostability. While 5-TAMRA shows a lower quantum yield (37-39%) than the Cy3B derivative (ca. 57%), its photostability is considerably higher compared to Cy3B. Generally, the impact of the protein on the photophysics is low. However, on prolonged illumination, both fluorescent dyes undergo a photocatalytic reaction with tryptophan residues of BSA mediated by sensitized singlet oxygen resulting in a tryptophan photoproduct with an absorption maximum around 330 nm. The overall results of this work will assist in choosing the right dye for the labeling of bioactive compounds, and the study demonstrates that experiments performed with 5-TAMRA or Cy3B-labeled compounds in a biological environment may be influenced by photochemical modification of experimentally relevant proteins at aromatic amino acid residues.