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Gap-graded aggregate combined with asphalt rubber presents a high-performance alternative for roads with heavy traffic loads, offering advantages over conventional mixtures in terms of permanent deformation (rutting), fatigue life, and texture. In this study, the conventional filler in the well-established mixture was substituted with sugarcane bagasse bottom ash (SCBA) at a proportion of 5% of the total mineral aggregates. The objective was to enhance the mechanical performance of the asphalt coating while ensuring proper disposal of this waste material. Compared to conventional filler, SCBA is less dense, has smaller dimensions, and exhibits greater roughness, thereby affecting the volumetric parameters of the Marshall mix design. Consequently, the volume of voids in mineral aggregates and voids filled with asphalt increased while maintaining the same volume of air voids (5.3%). Consequently, there was a notable increase in Marshall Stability (40%) and Indirect Tensile Test (22%) mechanical parameters. Following laboratory analysis, the modified mixtures were applied as asphalt coating on a high-traffic highway (BR-158). Field specimens revealed an 18% increase in the Resilience Modulus (4088 MPa; 3478 MPa). Additionally, its Flow Number exhibited a 73% increase (16,707; 9681), and its permanent deformation rate was 28% lower within 10,000 cycles in the dynamic creep test. This was further supported by an 11% reduction in permanent deformation rate in the Hamburg Wheel Tracking Device (HWTD) within 20,000 cycles (3.2 mm; 3.6 mm). In conclusion, the partial replacement of conventional filler with sugarcane bagasse ash within the established granulometric range has demonstrated technical feasibility both in laboratory and field settings., (© 2024. The Author(s).)

Based on the circular code theory, we define a new function f that quantifies the property of reading frame retrieval (RFR) of genes from their codon usage. This RFR function f is computed on a massive scale in genes of genomes of bacteria, eukaryotes and archaea. By expressing f as a function of the mean number [Formula: see text] of codons per gene, a "universal" property is identified, whatever the kingdom: the reading frame retrieval is enhanced in large genes. By investigating this property according to the theory developed, a Spearman's rank correlation with a strong negative coefficient is observed between the codon usage dispersion d (from the uniform codon distribution [Formula: see text]) and the RFR function f, whatever the kingdom (p-values [Formula: see text] in bacteria, [Formula: see text] in eukaryotes and [Formula: see text] in archaea). Thus, the reading frame retrieval is enhanced with the codon usage dispersion. Furthermore, this approach identifies a "genome centre" from which emerge two distinct "genome arms": an upper arm and a lower arm, respectively, above and below the linear regression. The RFR function by itself or combined with classical methods (alignment, phylogeny) could also be a new approach to classify the genomes in the future., (© 2023. The Author(s), under exclusive licence to Society for Mathematical Biology.)

A code X is (⩾k)-circular if every concatenation of words from X that admits, when read on a circle, more than one partition into words from X, must contain at least k+1 words. In other words, the reading frame retrieval is guaranteed for any concatenation of up to k words from X. A code that is (⩾k)-circular for all integers k is said to be circular. Any code is (⩾0)-circular and it turns out that a code of trinucleotides is circular as soon as it is (⩾4)-circular. A code is k-circular if it is (⩾k)-circular and not (⩾k+1)-circular. Due to the explosive combinatorics of trinucleotide k-circular codes, we developed three classes of algorithms based on: (i) the smallest directed cycles (directed girth) in graphs; (ii) the eigenvalues of matrices; and (iii) the files that incrementally save partial results. These different approaches also allow us to verify the computational results obtained. We determine here the growth functions of trinucleotide k-circular codes, k varying between 0 and 4, in the general case and in various particular cases: minimum, minimal, maximum, self-complementary k-, (k,k,k)- and self-complementary (k,k,k)-circular., (Copyright © 2022. Published by Elsevier B.V.)

A code X is (⩾k)-circular if every concatenation of words from X that admits, when read on a circle, more than one partition into words from X, must contain at least k+1 words. In other words, the reading frame retrieval is guaranteed for any concatenation of up to k words from X. A code that is (⩾k)-circular for all integers k is said to be circular. Any code is (⩾0)-circular and it turns out that a code of trinucleotides is circular as soon as it is (⩾4)-circular. A code is k-circular if it is (⩾k)-circular and not (⩾k+1)-circular. The theoretical aspects of trinucleotide k-circular codes have been developed in a companion article (Michel et al., 2022). Trinucleotide circular codes always retrieve the reading frame, leaving no ambiguous sequences. On the contrary, trinucleotide k-circular codes, for k∈{0,1,2,3} all have ambiguous sequences, for which the reading frame cannot always be retrieved. However, such a trinucleotide k-circular code is still able to retrieve the reading frame for a number of sequences, thereby exhibiting a partial circularity property. We describe this combinatorial property for each class of trinucleotide k-circular codes with k∈{0,1,2,3}. The circularity, i.e. the reading frame retrieval, is an ordinary property in genes. In order to consider the different cases of ambiguous sequences, we derive a new and general formula to measure the reading frame loss, whatever the trinucleotide k-circular code. This formula allows us to study the evolution of any trinucleotide k-circular code of (maximal) cardinality 20 to the genetic code, based on the reading frame retrieval property. We apply this approach to analyse the evolution of the trinucleotide circular code X observed in genes to the genetic code. The (⩾1)-circular codes of maximal size 20 necessarily have the same number of each nucleotide, specifically 15=3⋅20/4. This balanceness property can also be achieved by trinucleotide codes of cardinality 4,8,12 and 16. We call such trinucleotide codes balanced. We develop a general mathematical method to compute the number of balanced trinucleotide codes of each size, which also applies to self-complementary trinucleotide codes. We establish and quantify a relation between this balanceness property and the self-complementarity property. The combinatorial hierarchy of trinucleotide k-circular codes is updated with the growth function results. The numbers of amino acids coded by the trinucleotide k-circular codes are given for the cases maximal, minimal, self-complementary k-, (k,k,k)- and self-complementary (k,k,k)-circular., (Copyright © 2022. Published by Elsevier B.V.)

A code X is k-circular if any concatenation of at most k words from X, when read on a circle, admits exactly one partition into words from X. It is circular if it is k-circular for every integer k. While it is not a priori clear from the definition, there exists, for every pair [Formula: see text], an integer k such that every k-circular [Formula: see text]-letter code over an alphabet of cardinality n is circular, and we determine the least such integer k for all values of n and [Formula: see text]. The k-circular codes may represent an important evolutionary step between the circular codes, such as the comma-free codes, and the genetic code.

By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C 3 -self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes were investigated. By using a graph-theoretical approach of circular codes recently developed, we study mixed circular codes, which are the union of a dinucleotide circular code, a trinucleotide circular code and a tetranucleotide circular code. Maximal mixed circular codes of (di,tri)-nucleotides, (tri,tetra)-nucleotides and (di,tri,tetra)-nucleotides are constructed, respectively. In particular, we show that any maximal dinucleotide circular code of size 6 can be embedded into a maximal mixed (di,tri)-nucleotide circular code such that its trinucleotide component is a maximal C 3 -comma-free code. The growth function of self-complementary mixed circular codes of dinucleotides and trinucleotides is given. Self-complementary mixed circular codes could have been involved in primitive genetic processes., (Copyright © 2019 Elsevier Inc. All rights reserved.)