Functional Convergence Research Articles

Multifunctional flexible self-supporting film electrode for wearable energy-storage sensing system

Thriving digital information technologies are propelling the elegant convergence of aesthetics and functionality in wearable electronic devices. However, developing tiny wearable systems is challenging due to the integration of bulky, cumbersome, and hazardous power supply components. To address this issue, we design a wearable energy-storage sensing system that integrates a V2O5/MXene flexible film serving as both a cathode of zinc-ion microbatteries (ZIMBs) and a piezoresistive sensor. The flexible film, free of inert binder, enhances electrode utilization for higher energy densities. Characterised by its heterostructure and interconnected porous structure, the film provides a ultra-stability (18000 cycles at 30 A g−1) and excellent rate performance (167 mAh g−1 at 50 A g−1). Beyond that, the film with high flexibility can be assembled into planar ZIMBs via vacuum filtration. The ZIMBs, capable of reliable energy output, exhibit a decent area capacity of 531.6 μAh cm−2 under dynamic bending conditions. The adaptable ZIMB-sensing system integrated into the same plane offers better coupling effects. The uninterruptible power supply from microbattery ensures the system’s independence, which can transmit Morse code in real time and detect body motions with a swift response time of just 84 ms. Our design principle provides new ideas for the independent and miniaturized development of wearable electronics.

Decision-Making on Deferred Statistical Convergence of Measurable Functions of Two Variables

In this paper, we define and study strongly deferred Cesàro summable, strongly Cesàro summable, m-statistical convergence and m-deferred statistical convergence of real-valued Lebesgue measurable functions of two variables. Further, we present illustrative examples in support of our definitions. Also, we examine some properties and relations among these concepts under some restrictions. In addition, we present illustrative examples to show the essentiality of these restrictions.

Cooperative price-based demand response program for multiple aggregators based on multi-agent reinforcement learning and Shapley-value

Demand response (DR) plays an essential role in power system management. To facilitate the implementation of these techniques, many aggregators have appeared in response as new mediating entities in the electricity market. These actors exploit the technologies to engage customers in DR programs, offering grid services like load scheduling. However, the growing number of aggregators has become a new challenge, making it difficult for utilities to manage the load scheduling problem. This paper presents a multi-agent reinforcement Learning (MARL) approach to a price-based DR program for multiple aggregators. A dynamic pricing scheme based on discounts is proposed to encourage residential customers to change their consumption patterns. This strategy is based on a cooperative framework for a set of DR Aggregators (DRAs). The DRAs take advantage of a reward offered by a Distribution System Operator (DSO) for performing a peak-shaving over the total system aggregated demand. Furthermore, a Shapley-Value-based reward sharing mechanism is implemented to fairly determine the individual contribution and calculate the individual reward for each DRA. Simulation results verify the merits of the proposed model for a multi-aggregator system, improving DRAs’ pricing strategies considering the overall objectives of the system. Consumption peaks were managed by reducing the Peak-to-Average Ratio (PAR) by 15%, and the MARL mechanism’s performance was improved in terms of reward function maximization and convergence time, the latter being reduced by 29%.

Comparison of Convergence for Different Models and Loss Function: Evidence from Transformer, Diffusion and RNN

Abstract. With the development of science and technology, people are using machine learning as a method to make life easier. However, the performance corresponding to different models will produce different predictions and results for one thing. In order to improve the performance of the model, this paper investigates the influence of the learning rate hyperparameter on the model's performance, and demonstrates it through the convergence of the loss function. After experimental research, it has been found that different models exhibit significant differences in their performance when processing the same dataset. Meanwhile, different learning rates also have a significant impact on the performance of the model. Therefore, after selecting the correct model for machine learning, one should also adjust a relatively good hyperparameter to make the entire process smoother. Based on the analysis, one will gain a basic understanding of the optimal learning rates for transformer, diffusion, and RNN models when training MNIST. It is convenient for people to set better hyperparameters and obtain better prediction and decision-making results when using these three models, so that one can demonstrate better performance when using these three models.

К МЕТОДИКЕ ФОРМИРОВАНИЯ ЦИФРОВОГО ДВОЙНИКА ТЕХНОЛОГИЧЕСКОГО ПРОЦЕССА СУШКИ ОРГАНИЧЕСКИХ СЕМЯН ТИМОФЕЕВКИ

An important specific feature of the functioning of machines and equipment in the technologies of post-harvest processing of grain and seeds is the probabilistic variability of external conditions that negatively affect the efficiency of their work. The drying process is also characterized by non-stationarity in its probabilistic and statistical characteristics. The methods of forming digital twins of stationary processes are quite well mastered, but the construction of digital twins of non-stationary processes is a much more complex task, the solution of which requires taking into account the nature of non-stationarity, as well as the features and internal structure of the processes being modeled. The purpose of the research is to build a digital twin of the non-stationary process of drying timothy seeds and assess the reliability of the resulting model. The experimental data were obtained by drying Leningradskaya 204 timothy grass seeds from the field organic crop rotation using a universal drying unit with a Fauna PMDR4 digital seed moisture meter equipped with submersible flow sensors. As a result of the experimental studies, realizations of random processes of change in seed moisture content at the final stage of drying were obtained for constructing mathematical models using statistical identification methods. Discrete analogs of the processes under study were constructed using experimental correlation functions approximated by the corresponding functions to obtain the parameters of the modeling recurrent equations. The considered algorithm for modeling the dryer operation allows reproducing processes of unlimited length and modeling various conditions and operating modes to find the specified optima for quality, energy consumption and environmental friendliness. The accuracy of the simulation results was determined based on the convergence of the moment functions of the experimental and modeled technological processes. Estimates of statistical characteristics of the simulated process of drying timothy grass seeds with 95% probability correspond to statistical estimates of the drying process obtained in the course of experimental studies, and the graphs of their normalized correlation functions clearly confirm the identity of the processes. The obtained mathematical dependencies of the technological process of drying organic timothy grass seeds are its digital twin, allowing the methods of simulation modeling to solve optimization problems.

Kähler–Einstein metrics on families of Fano varieties

Abstract Given a one-parameter family of ℚ-Fano varieties such that the central fiber admits a unique Kähler–Einstein metric, we provide an analytic method to show that the neighboring fiber admits a unique Kähler–Einstein metric. Our results go beyond by establishing uniform a priori estimates on the Kähler–Einstein potentials along fully degenerate families of ℚ-Fano varieties. In addition, we show the continuous variation of these Kähler–Einstein currents and establish uniform Moser–Trudinger inequalities and uniform coercivity of the Ding functionals. Central to our article is introducing and studying a notion of convergence for quasi-plurisubharmonic functions within families of normal Kähler varieties. We show that the Monge–Ampère energy is upper semi-continuous with respect to this topology, and we establish a Demailly–Kollár result for functions with full Monge–Ampère mass.

Refractive and ocular motor status in autistic adults without learning disabilities: an exploratory study

ABSTRACT Clinical relevance Refractive and ocular motor anomalies may be more prevalent among autistic adults without learning disabilities, compared to a non-autistic clinical population. In line with current guidance, optometrists should exclude these anomalies prior to prescribing tinted lenses. Background Autistic adults report various visual experiences with largely negative consequences on daily living. Some of these overlap with symptoms of refractive and ocular motor anomalies. Therefore, this study investigated refractive and ocular motor status, and pattern glare, in autistic adults without learning disabilities. The impact of appropriate treatment on visual experiences was explored. Methods Twenty four autistic adults, aged 19–67 years, underwent an eye examination involving refraction, ocular motor and pattern glare assessments. Based on pre-determined criteria, anomalies were treated with spectacles, orthoptic exercises, or tinted lenses. Participants completed three questionnaires (Glasgow Sensory Questionnaire, Visual Function Index and Convergence Insufficiency Symptoms Survey) at the start and end of the study to assess the impact of treatment. Results Relative to population norms, a notable proportion of participants had: a significant change in refractive correction (83.3%); accommodative infacility (72.7%); convergence insufficiency (37.5%); uncompensated distance dissociated heterophoria (33.3%); significant accommodative inaccuracy (27.2%); and positive pattern glare (25%). All participants required treatment. 16.7% were given orthoptic exercises only. New spectacles were dispensed to 79.2%, followed by 16.7% requiring orthoptic exercises and 4.2% dispensed tinted lenses. Questionnaire scores did not significantly change post-treatment. Conclusion This exploratory study suggests autistic adults may be more likely to present with refractive, ocular motor and pattern glare issues. Impacts on autistic visual sensory experiences, vision-related quality of life and visual function remain unclear. Pattern Glare Test scores of autistic adults appear to be reduced by appropriate refractive and/or ocular motor management. Therefore, optometrists should take a conservative approach, managing refraction and ocular motor status of autistic patients prior to considering tinted lenses.

Mechanisms of epigenomic and functional convergence between glucocorticoid- and IL4-driven macrophage programming

Macrophages adopt distinct phenotypes in response to environmental cues, with type-2 cytokine interleukin-4 promoting a tissue-repair homeostatic state (M2IL4). Glucocorticoids (GC), widely used anti-inflammatory therapeutics, reportedly impart a similar phenotype (M2GC), but how such disparate pathways may functionally converge is unknown. We show using integrative functional genomics that M2IL4 and M2GC transcriptomes share a striking overlap mirrored by a shift in chromatin landscape in both common and signal-specific gene subsets. This core homeostatic program is enacted by transcriptional effectors KLF4 and the glucocorticoid receptor, whose genome-wide occupancy and actions are integrated in a stimulus-specific manner by the nuclear receptor cofactor GRIP1. Indeed, many of the M2IL4:M2GC-shared transcriptomic changes were GRIP1-dependent. Consistently, GRIP1 loss attenuated phagocytic activity of both populations in vitro and macrophage tissue-repair properties in the murine colitis model in vivo. These findings provide a mechanistic framework for homeostatic macrophage programming by distinct signals, to better inform anti-inflammatory drug design.

Applications of Novel Microscale and Nanoscale Materials for Theranostics: From Design to Clinical Translation.

The growing global prevalence of chronic diseases has highlighted the limitations of conventional drug delivery methods, which often suffer from non-specific distribution, systemic toxicity, and poor bioavailability. Microscale and nanoscale materials have emerged as innovative solutions, offering enhanced targeting, controlled release, and the convergence of therapeutic and diagnostic functions, referred to as theranostics. This review explores the design principles, mechanisms of action, and clinical applications of various novel micro- and nanomaterials in diseases such as cancer, cardiovascular disorders, and infectious diseases. These materials enable real-time monitoring of therapeutic responses and facilitate precision medicine approaches. Additionally, this paper addresses the significant challenges hindering clinical translation, including biocompatibility, potential toxicity, and regulatory issues. Ongoing clinical trials demonstrate the potential of nanomaterials in theranostic applications, but further research is needed to overcome the barriers to widespread clinical adoption. This work aims to contribute to the acceleration of integrating nanomedicine into clinical practice, ultimately enhancing the efficacy and safety of therapeutic interventions.

Analysis and comparison of high-performance computing solvers for minimisation problems in signal processing

Several physics and engineering applications involve the solution of a minimisation problem to compute an approximation of the input signal. Modern hardware and software use high-performance computing to solve problems and considerably reduce execution time. In this paper, different optimisation methods are compared and analysed for the solution of two classes of non-linear minimisation problems for signal approximation and denoising with different constraints and involving computationally expensive operations, i.e., (i) the global optimisers divide rectangle-local and the improved stochastic ranking evolution strategy, and (ii) the local optimisers principal axis, the Limited-memory Broyden, Fletcher, Goldfarb, Shanno, and the constrained optimisation by linear approximations. The proposed approximation and denoising minimisation problems are attractive due to their numerical and analytical properties, and their analysis is general enough to be extended to most signal-processing problems. As the main contribution and novelty, our analysis combines an efficient implementation of signal approximation and denoising on arbitrary domains, a comparison of the main optimisation methods and their high-performance computing implementations, and a scalability analysis of the main algebraic operations involved in the solution of the problem, such as the solution of linear systems and singular value decomposition. Our analysis is also general regarding the signal processing problem, variables, constraints (e.g., bounded, non-linear), domains (e.g., structured and unstructured grids, dimensionality), high-performance computing hardware (e.g., cloud computing, homogeneous vs. heterogeneous). Experimental tests are performed on the CINECA Marconi100 cluster at the 26th position in the “top500” list and consider several parameters, such as functional computation, convergence, execution time, and scalability. Our experimental tests are discussed on real-case applications, such as the reconstruction of the solution of the fluid flow field equation on an unstructured grid and the denoising of a satellite image affected by speckle noise. The experimental results show that principal axis is the best optimiser in terms of minima computation: the efficiency of the approximation is 38% with 256 processes, while the denoising has 46% with 32 processes.

The microbiome and metatranscriptome of a panel from the Sarracenia mapping population reveal complex assembly and function involving host influence.

Sarracenia provide an optimal system for deciphering the host-microbiome interactions at various levels. We analyzed the pitcher microbiomes and metatranscriptomes of the parental species, and F1 and F2 generations from the mapping population (Sarracenia purpurea X Sarracenia psittacina) utilizing high-throughput sequencing methods. This study aimed to examine the host influences on the microbiome structure and function and to identify the key microbiome traits. Our quality datasets included 8,892,553 full-length bacterial 16s rRNA gene sequences and 65,578 assembled metatranscripts with microbial protein annotations. The correlation network of the bacterial microbiome revealed the presence of 3-7 distinct community clusters, with 8 hub and 19 connector genera. The entire microbiome consisted of viruses, bacterial, archaea, and fungi. The richness and diversity of the microbiome varied among the parental species and offspring genotypes despite being under the same greenhouse environmental conditions. We have discovered certain microbial taxa that are genotype-enriched, including the community hub and connector genera. Nevertheless, there were no significant differences observed in the functional enrichment analysis of the metatranscriptomes across the different genotypes, suggesting a functional convergence of the microbiome. We found that the pitcher microcosm harbors both rhizosphere and phyllosphere microbiomes within its boundaries, resulting in a structurally diverse and functionally complex microbiome community. A total of 50,424 microbial metatranscripts were linked to plant growth-promoting microbial proteins. We show that this complex pitcher microbiome possesses various functions that contribute to plant growth promotion, such as biofertilization, bioremediation, phytohormone signaling, stress regulation, and immune response stimulation. Additionally, the pitcher microbiome exhibits traits related to microbe-microbe interactions, such as colonization of plant systems, biofilm formation, and microbial competitive exclusion. In summary, the demonstrated taxonomical divergence and functionally convergence of the pitcher microbiome are impacted by the host genetics, making it an excellent system for discovering novel beneficial microbiome traits.

Evolution from mixed to fixed handedness in mirror-image flowers: insights from adaptive dynamics.

Mirror-image flowers (enantiostyly) involve a form of sexual asymmetry in which a flower's style is deflected either to the left or right side, with a pollinating anther orientated in the opposite direction. This curious floral polymorphism, which was known but not studied by Charles Darwin, occurs in at least 11 unrelated angiosperm families and represents a striking example of adaptive convergence in form and function associated with cross-pollination by insects. In several lineages, dimorphic enantiostyly (one stylar orientation per plant, both forms occurring within populations) has evolved from monomorphic enantiostyly, in which all plants can produce both style orientations. We use a modelling approach to investigate the emergence of dimorphic enantiostyly from monomorphic enantiostyly under gradual evolution. We show using adaptive dynamics that depending on the balance between inbreeding depression following geitonogamy, pollination efficiency and plant density, dimorphism can evolve from an ancestral monomorphic population. In general, the newly emergent dimorphic population is stable against invasion of a monomorphic mutant. However, our model predicts that under certain ecological conditions, e.g., a decline of pollinators, dimorphic enantiostyly may revert to a monomorphic state. We demonstrate using population genetics simulations that the observed evolutionary transitions are possible assuming a plausible genetic architecture.

Modularity of the Schur index, modular differential equations, and high-temperature asymptotics

In this paper we analytically explore the modularity of the flavored Schur index of 4d N=2 superconformal field theories. We focus on the A1 theories of class-S and N=4 theories with SU(N) gauge group. We work out the modular orbit of the flavored index and defect index, compute the dimension of the space spanned by the orbit, and provide complete basis for computing modular transformation matrices. The dimension obtained from the flavored analysis predicts the minimal order of the unflavored modular differential equation satisfied by the unflavored Schur index. With the help of modularity, we also study analytically the high temperature asymptotics of the Schur index. In the high temperature limit τ→+i0, we identified the (defect) Schur index of the genus-zero A1 theories of class S with the S3 partition function of the SU(2)×U(1)n star-shaped quiver (with Wilson line insertion). In the identification, we observe an interesting relation between the linear-independence of defect indices and the convergence of the Wilson line partition functions. Published by the American Physical Society 2024

On formal series solutions to 4th-order quadratic homogeneous differential equations and their convergence

Abstract It is known that all τ functions of the Painlevé equations satisfy the fourth-order quadratic differential equation. Among them, for the III, V, and VI equations, it is possible to express the formal series solutions combinatorially by using conformal blocks. In this paper, we show the convergence of the formal series, including the solutions of more general equations. The convergence of the conformal block function also follows in the case c = 1 by the absolute convergence of τ series, since it is a partial sum of the τ series. We also characterized the form of a homogeneous quadratic equation with a series solution similar to the tau functions of the Painlevé equations.

HLA-C Peptide Repertoires as Predictors of Clinical Response during Early SARS-CoV-2 Infection.

The human leukocyte antigen (HLA) system plays a pivotal role in the immune response to viral infections, mediating the presentation of viral peptides to T cells and influencing both the strength and specificity of the host immune response. Variations in HLA genotypes across individuals lead to differences in susceptibility to viral infection and severity of illness. This study uses observations from the early phase of the COVID-19 pandemic to explore how specific HLA class I molecules affect clinical responses to SARS-CoV-2 infection. By analyzing paired high-resolution HLA types and viral genomic sequences from 60 patients, we assess the relationship between predicted HLA class I peptide binding repertoires and infection severity as measured by the sequential organ failure assessment score. This approach leverages functional convergence across HLA-C alleles to identify relationships that may otherwise be inaccessible due to allelic diversity and limitations in sample size. Surprisingly, our findings show that severely symptomatic infection in this cohort is associated with disproportionately abundant binding of SARS-CoV-2 structural and non-structural protein epitopes by patient HLA-C molecules. In addition, the extent of overlap between a given patient's predicted HLA-C and HLA-A peptide binding repertoires correlates with worse prognoses in this cohort. The findings highlight immunologic mechanisms linking HLA-C molecules with the human response to viral pathogens that warrant further investigation.

A functional screen for ubiquitin regulation identifies an E3 ligase secreted by Pseudomonas aeruginosa.

Ubiquitin signaling controls many aspects of eukaryotic biology, including targeted protein degradation and immune defense. Remarkably, invading bacterial pathogens have adapted secreted effector proteins that hijack host ubiquitination to gain control over host responses. These ubiquitin-targeted effectors can exhibit, for example, E3 ligase or deubiquitinase activities, often without any sequence or structural homology to eukaryotic ubiquitin regulators. Such convergence in function poses a challenge to the discovery of additional bacterial virulence factors that target ubiquitin. To overcome this, we have developed a workflow to harvest natively secreted bacterial effectors and functionally screen them for ubiquitin regulatory activities. After benchmarking this approach on diverse ligase and deubiquitinase activities from Salmonella Typhimurium, Enteropathogenic Escherichia coli, and Shigella flexneri, we applied it to the identification of a cryptic E3 ligase activity secreted by Pseudomonas aeruginosa. We identified an unreported P. aeruginosa E3 ligase, which we have termed Pseudomonas Ub ligase 1 (PUL-1), that resembles none of the other E3 ligases previously established in or outside of the eukaryotic system. Importantly, in an animal model of P. aeruginosa infection, PUL-1 ligase activity plays an important role in regulating virulence. Thus, our workflow for the functional identification of ubiquitin-targeted effector proteins carries promise for expanding our appreciation of how host ubiquitin regulation contributes to bacterial pathogenesis.

An Intelligent Proofreading for Remote Skiing Actions Based on Variable Shape Basis

AbstractThe current proofreading algorithms for action regulation mainly recover the 3D structure and action information of non-rigid objects from image sequences by factorization. Most of algorithms assume that the camera model is an affine model. This assumption only holds if the size and depth of the object change very little relative to the distance from the object to the camera, which is in the case of fixed-shape basis. When the object is very close to the camera, this assumption causes a large reconstruction error. This paper solves this problem by the intelligent proofreading algorithms for remote skiing teaching actions based on variable shape basis. Firstly, the improved Retinex algorithm is used to enhance the multi-frame video images of skiing actions to make the action details more prominent. Then, measurement matrix is calculated after eliminating the translation vector by coordinate transformation. Under the condition of rank constraint, the measurement matrix is decomposed by singular value decomposition algorithm, and the correct shape basis structure of 3D action features can be obtained by using the variable shape basis. Finally, by randomly initializing a parameter, the optimized parameter and the least square algorithm are used to optimize the randomly initialized parameter further. The iteration until the convergence of the objective function can be used to calculate the deformation degree of the actions. The test results show that this algorithm improves the proofreading accuracy of action regulation in skiing teaching, and the proofreading results of various uploaded sliding actions are correct, which can be applied to remote skiing teaching and community learning.

Patterns and drivers in the functional diversity decomposition of invaded stream fish communities

AbstractAimThe assembly of real‐world ecological communities in human‐modified landscapes is influenced by a complex interplay of spatial, temporal, environmental and invasion gradients. However, understanding the relative importance of these drivers and their interactions in shaping functional assembly remains elusive. Our study aimed to investigate the relative influence of these drivers on the functional assembly of a stream fish metacommunity.LocationStreams of the Lake Balaton catchment, Hungary.MethodsWe analysed a long‐term (18‐year) dataset of the stream fish metacommunity, focusing on changes in functional diversity (Q), redundancy (R) and species dominance (D). Ternary diagrams were utilized to decompose functional diversity into Q, R and D components and to visualize diversity patterns. Linear mixed‐effect regression and separate structural equation models were employed to identify significant drivers of Q, R and D.ResultsNative fish communities exhibited low functional diversity (Q) but high redundancy (R) and dominance (D), indicating functional convergence and dominance. Stream habitat size, network position and associated spatial, physical and chemical gradients emerged as consistently significant drivers of D and R. Changes in Q were additionally linked to non‐native community properties and subtle shifts in land use and within‐stream habitat characteristics.Main ConclusionsOur findings suggest that both environmental filtering and interspecies interactions, particularly trait similarity between invaders and natives shape functional assembly of stream fish metacommunities. Despite minimal temporal directional changes, environmental drivers predominantly influence long‐term diversity patterns of native fish communities, overshadowing invasion effects. Our findings underscore the importance of considering both environmental filtering mechanisms and interspecies interactions in understanding functional assembly. Additionally, the joint application of diversity decomposition frameworks with predictive modelling provides comprehensive insight into patterns of functional diversity and assembly across ecological communities.

Microbial bases of herbivory in beetles.

The ecological radiation of herbivorous beetles is among the most successful in the animal kingdom. It coincided with the rise and diversification of flowering plants, requiring beetles to adapt to a nutritionally imbalanced diet enriched in complex polysaccharides and toxic secondary metabolites. In this review, we explore how beetles overcame these challenges by coopting microbial genes, enzymes, and metabolites, through both horizontal gene transfer (HGT) and symbiosis. Recent efforts revealed the functional convergence governing both processes and the unique ways in which microbes continue to shape beetle digestion, development, and defense. The development of genetic and experimental tools across a diverse set of study systems has provided valuable mechanistic insights into how microbes spurred metabolic innovation and facilitated an herbivorous transition in beetles.

Diverse Origins of Near-Identical Antifreeze Proteins in Unrelated Fish Lineages Provide Insights Into Evolutionary Mechanisms of New Gene Birth and Protein Sequence Convergence.

Determining the origins of novel genes and the mechanisms driving the emergence of new functions is challenging yet crucial for understanding evolutionary innovations. Recently evolved fish antifreeze proteins (AFPs) offer a unique opportunity to explore these processes, particularly the near-identical type I AFP (AFPI) found in four phylogenetically divergent fish taxa. This study tested the hypothesis of protein sequence convergence beyond functional convergence in three unrelated AFPI-bearing fish lineages. Through comprehensive comparative analyses of newly sequenced genomes of winter flounder and grubby sculpin, along with available high-quality genomes of cunner and 14 other related species, the study revealed that near-identical AFPI proteins originated from distinct genetic precursors in each lineage. Each lineage independently evolved a de novo coding region for the novel ice-binding protein while repurposing fragments from their respective ancestors into potential regulatory regions, representing partial de novo origination-a process that bridges de novo gene formation and the neofunctionalization of duplicated genes. The study supports existing models of new gene origination and introduces new ones: the innovation-amplification-divergence model, where novel changes precede gene duplication; the newly proposed duplication-degeneration-divergence model, which describes new functions arising from degenerated pseudogenes; and the duplication-degeneration-divergence gene fission model, where each new sibling gene differentially degenerates and renovates distinct functional domains from their parental gene. These findings highlight the diverse evolutionary pathways through which a novel functional gene with convergent sequences at the protein level can evolve across divergent species, advancing our understanding of the mechanistic intricacies in new gene formation.