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We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics. [ABSTRACT FROM AUTHOR]

The orthogonal time frequency space (OTFS) modulation technique can provide reliable communication in time-varying channels. Due to the dispersive characteristics of underwater acoustic channels, this paper proposes an OTFS-IM underwater acoustic communication system based on Hamming distance optimization to reduce the impact of dispersion in underwater acoustic communication. Firstly, the OTFS-IM underwater acoustic communication system is introduced, which introduces index modulation into the Delay–Doppler (DD) domain to make the OTFS system have stronger anti-Delay–Doppler capability. In contrast, since there is index sequence redundancy in a specific index combination, a Hamming distance optimization model is used to eliminate the redundant combination in the specific index combination sequence and further improve the bit error rate performance of the system. In addition, the Hamming distance optimized OTFS-IM underwater acoustic communication system is verified by simulation analysis. The results show that the proposed Hamming distance optimized OTFS-IM can achieve more reliable bit error rate performance. [ABSTRACT FROM AUTHOR]

In this paper, by using the Hamming distance, we establish a relation between quantum error-correcting codes ((N , K , d + 1)) s and orthogonal arrays with orthogonal partitions. Therefore, this is a generalization of the relation between quantum error-correcting codes ((N , 1 , d + 1)) s and irredundant orthogonal arrays. This relation is used for the construction of pure quantum error-correcting codes. As applications of this method, numerous infinite families of optimal quantum codes can be constructed explicitly such as ((3 , s , 2)) s for all s i ≥ 3 , ((4 , s 2 , 2)) s for all s i ≥ 5 , ((5 , s , 3)) s for all s i ≥ 4 , ((6 , s 2 , 3)) s for all s i ≥ 5 , ((7 , s 3 , 3)) s for all s i ≥ 7 , ((8 , s 2 , 4)) s for all s i ≥ 9 , ((9 , s 3 , 4)) s for all s i ≥ 11 , ((9 , s , 5)) s for all s i ≥ 9 , ((10 , s 2 , 5)) s for all s i ≥ 11 , ((11 , s , 6)) s for all s i ≥ 11 , and ((12 , s 2 , 6)) s for all s i ≥ 13 , where s = s 1 ⋯ s n and s 1 , ... , s n are all prime powers. The advantages of our approach over existing methods lie in the facts that these results are not just existence results, but constructive results, the codes constructed are pure, and each basis state of these codes has far less terms. Moreover, the above method developed can be extended to construction of quantum error-correcting codes over mixed alphabets. [ABSTRACT FROM AUTHOR]

The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R : = F 4 [ v ] / 〈 v 3 〉 . We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length n. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes. [ABSTRACT FROM AUTHOR]

This work presents a quantum associative memory (Alpha-Beta HQAM) that uses the Hamming distance for pattern recovery. The proposal combines the Alpha-Beta associative memory, which reduces the dimensionality of patterns, with a quantum subroutine to calculate the Hamming distance in the recovery phase. Furthermore, patterns are initially stored in the memory as a quantum superposition in order to take advantage of its properties. Experiments testing the memory's viability and performance were implemented using IBM's Qiskit library. [ABSTRACT FROM AUTHOR]

The use of eye movement as a biometric is a new biometric technology that is now in competition with many other technologies such as the fingerprint, face recognition, ear recognition and many others. Problems encountered with these authentication methods such as passwords and tokens have led to the emergence of biometric authentication techniques. Biometric authentication involves the use of physical or behavioral characteristics to identify people. In biometric authentication, feature extraction is a very vital stage, although some of the extracted features that are not very useful may lead to the degradation of the biometric system performance. Object selection using eye movement as a technique for biometric authentication was proposed for this study. To achieve this, an experiment for collecting eye movement data for biometric purposes was conducted. Eye movement data were measured from twenty participants during choosing and finding of still objects. The eye-tracking equipment used was able to measure eye-movement data. The model proposed in this paper aimed to create a template from these observations that tried to assign a unique binary signature for each enrolled user. Error correction is used in authenticating a user who submits an eye movement sample for enrollment. The XORed Biometric template is further secured by multiplication with an identity matrix of size (n × n). These results show positive feedback on this model as individuals can be uniquely identified by their eye movement features. The use of hamming distance as additional verification helper increased model performance significantly. The proposed scheme has a 37% FRR and a 27% FAR based on the 400 trials, which are very promising results for future improvements. [ABSTRACT FROM AUTHOR]

The main goal of our work is to show how ideas change in social networks. Our analysis is based on three concepts: (i) temporal networks, (ii) the Axelrod model of culture dissemination, (iii) the garbage can model of organizational choice. The use of the concept of temporal networks allows us to show the dynamics of ideas spreading processes in networks, thanks to the analysis of contacts between agents in networks. The Axelrod culture dissemination model allows us to use the importance of cooperative behavior for the dynamics of ideas disseminated in networks. In the third model decisions on solutions of problems are made as an outcome of sequences of pseudorandom numbers. The origin of this model is the Herbert Simon's view on bounded rationality. In the Axelrod model, ideas are conveyed by strings of symbols. The outcome of the model should be the diversity of evolving ideas as dependent on the chain length, on the number of possible values of symbols and on the threshold value of Hamming distance which enables the combination. [ABSTRACT FROM AUTHOR]