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.

Trees for real-time media are typically created using procedural algorithms and then baked to a polygon format, requiring large amounts of memory. We propose a novel procedural system and model for generating and rendering realistic trees and similar vegetation specifically tailored to run in real-time on GPUs. By using GPU work graphs with mesh nodes, we render gigabytes-worth of tree geometry from kilobytes of generation code every frame exclusively on the GPU. Contrary to prior work, our method combines instant in-engine artist authoring, continuous frame-specific level of detail and tessellation, highly detailed animation, and seasonal details like blossoms, fruits, and snow. Generating the unique tree geometries of our teaser test scene and rendering them to the G-buffer takes 3.13 ms on an AMD Radeon RX 7900 XTX.