There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges and thus allow a better approximation of the data entropy. This class includes three prominent members: conventional arithmetic coding, range coding, and coding based on asymmetric numeral systems. To determine the correct symbol in the decoder, each of these methods requires the comparison of a state variable with subinterval boundaries.

In adaptive operation, considering varying symbol statistics, an array of interval boundaries must additionally be kept up to date. The larger the symbol alphabet, the more time-consuming both the search for the correct subinterval and the updating of interval borders become. These entropy coding methods play an important role in all data transmission and storage applications, and optimising speed can be crucial.

Based on detailed pseudo-code, different known and proposed approaches are discussed to speed up the symbol search in the decoder and the adaptation of the array of interval borders, both depending on the chosen alphabet size. It is shown that reducing the big O complexity in practical implementations does not necessarily lead to an acceleration, especially if the alphabet size is too small. For example, the symbol determination at the decoder shows an expected low cpu-clock ratio (O(logn) algorithm versus O(n) algorithm) of about 0.62 for an alphabet with 256 symbols. However, for an alphabet with only 4 symbols, this ratio is 1.05, that means the algorithm with lower theoretical complexity executes slightly faster here. In adaptive compression mode, the binary indexing (BI) method proves to be superior when considering the overall processing time. Although the symbol search (in the decoder) takes longer than using other algorithms (e.g. cpu-clock ratio BI/O(logn) is 1.57), the faster updating of the array of interval borders more than compensates for this disadvantage (total ratio BI/O(logn) is 0.72). A variant of the binary indexing method is proposed, which is more flexible and has a partially lower complexity than the original approach. Specifically, the rescaling of cumulative counts can be reduced in its complexity from O(4n+[log2(n)−2]·n/2) to O(3n).

Results from studies indicate that starting a sustainability-oriented business is associated with specific challenges. Our aim therefore was to investigate the mindset and needs of sustainable entrepreneurs, focusing on their motivations, challenges and support requirements during the establishment of sustainability-oriented start-ups. The focus was on respective start-ups in two rural and rather conservative regions in Germany. Together with an interdisciplinary group of students at a university course, we conducted guideline-based interviews with N=14 founders of sustainability-oriented enterprises from different business sectors. The interviews were analysed using a category system aligned with the study’s objectives. Findings highlight that sustainable thinking is deeply embedded in the respondents' values, often prioritizing ethical considerations over profit maximization. Many of them face a tension between sustainability and profitability, as sustainable products tend to be more expensive, and there is uncertainty about the availability of willing customers. Moreover, the research identifies specific support needs, including assistance with bureaucratic processes, networking opportunities, and strategies for customer acquisition. We derive implications for higher education institutions’ education as well as for external programmes to support (prospective) sustainable entrepreneurs.

Aging is a complex process that significantly contributes to age-related diseases and poses significant challenges for effective interventions, with few holistic anti-aging approaches successfully reversing its signs. Heterochronic parabiosis studies illuminated the potential for rejuvenation through blood-borne factors, yet the specific drivers including underlying mechanisms remain largely unknown and until today insights have not been successfully translated to humans. In this study, we were able to recreate rejuvenation of the human skin via systemic factors using a microphysiological system including a 3D skin model and a 3D bone marrow model. Addition of young human serum in comparison to aged human serum resulted in an improvement of proliferation and a reduction of the biological age as measured by methylation-based age clocks in the skin tissue. Interestingly, this effect was only visible in the presence of bone marrow-derived cells. Further investigation of the bone marrow model revealed changes in the cell population in response to young versus aged human serum treatment. Using proteome analysis, we identified 55 potential systemic rejuvenating proteins produced by bone marrow-derived cells. For seven of these proteins, we were able to verify a rejuvenating effect on human skin cells using hallmarks of aging assays, supporting their role as systemic factors rejuvenating human skin tissue.