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For three specific singular perturbed three-component reaction–diffusion systems that admit N-spike solutions in one of the components on a finite domain, we present a detailed analysis for the dynamics of temporal oscillations in the spike positions. The onset of these oscillations is induced by N Hopf bifurcations with respect to the translation modes that are excited nearly simultaneously. To understand the dynamics of N spikes in the vicinity of Hopf bifurcations, we combine the center manifold reduction and the matched asymptotic method to derive a set of ordinary differential equations (ODEs) of dimension 2N describing the spikes’ locations and velocities, which can be recognized as normal forms of multiple Hopf bifurcations. The reduced ODE system then is represented in the form of linear oscillators with weakly nonlinear damping. By applying the multiple-time method, the leading order of the oscillation amplitudes is further characterized by an N-dimensional ODE system of the Stuart–Landau type. Although the leading order dynamics of these three systems are different, they have the same form after a suitable transformation. On the basis of the reduced systems for the oscillation amplitudes, we prove that there are at most ⌊ N / 2 ⌋ + 1 stable equilibria, corresponding to ⌊ N / 2 ⌋ + 1 types of different oscillations. This resolves an open problem proposed by Xie et al. (Nonlinearity 34(8):5708–5743, 2021) for a three-component Schnakenberg system and generalizes the results to two other classic systems. Numerical simulations are presented to verify the analytic results. [ABSTRACT FROM AUTHOR]

Population migration within spatial structures significantly influences disease spread. Given the typically uneven environment, individuals randomly interact with various others, facilitating disease transmission over time. Complex networks are integrated into infectious disease models and effectively capture these contact dynamics. In this paper, we propose a two-delay networked SIR epidemic model featuring a Crowley-Martin type incidence rate and Holling III type treatment rate. The stability of three equilibria of the model is proved by analyzing the distribution of characteristic roots. When two delays change at the same time, the stable region of the equilibrium on delays plane and the existence of Hopf bifurcation are obtained by the method of stability switching curves. Furthermore, we calculate the normal form of Hopf bifurcation to obtain the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, numerical simulation on a small-world Watts-Strogatz network is performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A diffusive Lotka–Volterra competition system with memory-based diffusion is analyzed. The stability of the boundary steady states depends on memory-based self-diffusion but is independent of memory-based cross-diffusion. However, memory-based cross-diffusion induces instability in the constant coexistence state, increasing the complexity of the spatiotemporal dynamics of the system. We establish the critical conditions under which the constant coexistence state loses its stability through Turing bifurcation, Hopf bifurcation, and double-Hopf bifurcation. The normal form of the double-Hopf bifurcation is also derived. This allows us to prove the existence of an unstable spatially inhomogeneous quasi-periodic solution, and the coexistence of two types of stable spatially inhomogeneous periodic solutions with different wave numbers. In particular, a repulsive memory-based diffusion induces competing species to coexist in spatially segregated steady-state patterns, and an attractive memory-based diffusion can induce competing species to coexist in spatially segregated time-periodic patterns. [ABSTRACT FROM AUTHOR]

This study establishes a novel time-delay fractional SEIHR infectious disease model to investigate the effects of saturated incidence rates and time delays on different populations, including susceptibles, infected individuals, recovered individuals, and latent infected individuals. First, the existence and boundedness of the model's solutions are verified, confirming its well-posedness. Subsequently, the existence of equilibria is analyzed, and the impact of parameter variations on the system is explored by examining the equilibria ϵ 0 and ϵ ∗ , as well as the basic reproduction number R 0 . Additionally, the global dynamics of the equilibria are further analyzed using the Lyapunov method, while Hopf bifurcation theory is applied to explore the conditions under which the system shifts from stability to oscillatory behavior. Numerical simulations further validate the theoretical analysis, showing that time-delay effects significantly influence the system's responsiveness and the rate of disease transmission. Moreover, when the time delay τ crosses the critical threshold τ 0 , the system exhibits periodic oscillations. By predicting periodic fluctuations and incorporating memory effects and persistent influences, we can better control epidemics, emphasizing the importance of time-delay adjustments and enhancing the system's biological realism. [ABSTRACT FROM AUTHOR]

In this paper, we introduce spatial memory into a predator–prey model with herd behavior. Taking memory-based diffusion coefficient and average memory period of predators as control parameters, we obtain the stable conditions of the positive equilibrium of system and prove the existence of Hopf bifurcation. In addition, a double Hopf bifurcation occurs at the intersection of the nonhomogeneous Hopf bifurcation curves, and a spatially nonhomogeneous quasi-periodic pattern can be observed near the double Hopf bifurcation point by numerical simulation. [ABSTRACT FROM AUTHOR]

Implementing management systems in organisations of all types and sizes often raises the following question: "What benefits will this bring?" Initial resistance and criticism are common as potential challenges are identified during the implementation process. To address this, it is essential to highlight the advantages of these systems and engage stakeholders in supporting management efforts. While the planning, implementation, use, maintenance, auditing, and improvement of management systems are generally voluntary, certification is frequently driven by external factors, particularly customer demands. Employees also stand to gain significantly, with knowledge and information serving as valuable resources, especially for leveraging artificial intelligence. This article explores the management's readiness to adopt and fully utilise two management systems based on international standards: the ISO 30401 Knowledge management system (KMS) and the ISO/IEC 42001 Artificial intelligence management system (AIMS). Through interviews, we assess the challenges and solutions associated with implementing these systems, whether planned or partially adopted. The findings illustrate the synergistic benefits of integrating the KMS and AIMS, demonstrating how their combined use can enhance Integrated Management Systems (IMSs). Such integration supports comprehensive planning, operation, and performance evaluation of processes and services while also promoting continuous improvement. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of n-valued groups and studies their algebraic and topological properties. We explore a number of examples. An important class consists of those that we call n-coset groups; they arise as orbit spaces of groups G modulo a group of automorphisms with n elements. However, there are many examples that do not arise from this construction. We see that the theory of n-valued groups is distinct from that of groups with a given automorphism group. There are natural concepts of the action of an n-valued group on a space and of a representation in an algebra of operators. We introduce the (purely algebraic) notion of an n-Hopf algebra and show that the ring of functions on an n-valued group and, in the topological case, the cohomology has an n-Hopf algebra structure. The cohomology algebra of the classifying space of a compact Lie group admits the structure of an n-Hopf algebra, where n is the order of the Weyl group; the homology with dual structure is also an n-Hopf algebra. In general the group ring of an n-valued group is not an n-Hopf algebra but it is for an n-coset group constructed from an abelian group. Using the properties of n-Hopf algebras we show that certain spaces do not admit the structure of an n-valued group and that certain commutative n-valued groups do not arise by applying the n-coset construction to any commutative group. [ABSTRACT FROM AUTHOR]

This paper is concerned with the qualitative analysis of a diffusion SIR epidemic model with networked delay and nonlinear incidence rate. First, we prove the existence and uniqueness of the model by using the method of upper and lower solutions. Then, we prove that the trivial equilibrium (0, 0) is unstable; the disease‐free equilibrium (N, 0) is locally asymptotically stable if the reproduction number R0≤1 and unstable if R0>1; the endemic equilibrium (S∗, I∗) is locally asymptotically stable if R0≤R1 or if R1τ10∗. Moreover, when R1

High throughput in vitro assays for screening chemical hazards focus primarily on specific receptors that are linked with certain adverse outcome pathways, neglecting potential novel endpoints or pathways induced by emerging pollutants. Identifying target proteins that interact with pollutants contributes to finding potential molecular initiating events under the adverse outcome pathways framework. Mass spectrometry-based thermal proteome profiling (TPP) assays have permitted uncovering binding targets of pollutants across the whole proteome. Based on the principle that proteins are thermally stabilized after binding with chemicals, TPP differentiates protein targets by determining the soluble fraction of proteins that remain stable after heat stress. Thus, TPP facilitates qualitative and quantitative measurements of chemical-protein interactions (CPIs) without modifications on chemical structures or immobilization of target proteins. In this mini-review, we introduced the principles, development and procedures of TPP, and summarized its applications in identifying protein targets and speculating toxicity pathways for emerging pollutants in environmental toxicological studies. Additionally, since measurements of CPIs using TPP for multiple chemicals could be labor- and cost-intensive, machine learning-based modeling is a feasible alternative to dissect CPIs due to its capability to mine intrinsic properties determining CPIs. Therefore, the recent development of machine learning models for CPI prediction was reviewed. Lastly, we envisioned prospects of combining TPP data with machine learning for CPI prediction, and the possibility of applying TPP to interpret toxicity pathways and phenotypes generated from multi-omics data, to inform future environmental toxicological research on forecasting targets and outcomes for emerging pollutants. [ABSTRACT FROM AUTHOR]

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system's solutions, the research ensures the model's well-posedness, guaranteeing its mathematical soundness and practical relevance. The study calculates and evaluates the equilibrium points and the basic reproduction numbers R 0 1 and R 0 2 to understand the dynamic behavior of the model under different parameter settings. Through the application of the Lyapunov method, the research examines the asymptotic global stability of the system, determining whether it will converge to a particular equilibrium state over time. Furthermore, Hopf bifurcation theory is employed to investigate potential periodic solutions and bifurcation scenarios, highlighting how the system might shift from stability to periodic oscillations under certain conditions. By utilizing the Adams-Bashforth-Moulton numerical simulation method, the theoretical results are validated, reinforcing the conclusions and demonstrating the model's applicability in real-world contexts. It emphasizes the importance of fractional-order models in addressing epidemiological issues related to time delays (τ), individual heterogeneity (m, k), and memory effects (θ), offering greater accuracy compared with traditional integer-order models. In summary, this research provides a theoretical foundation and practical insights, enhancing the understanding and management of epidemic dynamics through fractional-order epidemic models. [ABSTRACT FROM AUTHOR]

This study examines the impact of Bisphenol A (BPA), a prevalent environmental estrogenic toxicant, on the ovarian development of mice. Mice were exposed to varying BPA doses from in utero to postnatal stages, up to weaning (day 21, PND 21) and puberty (day 45, PND 45). The BPA content in the serum of the offspring mice on PND 45 was higher than that of the mice sacrificed at PND 21. However, the ovary organ index of the mice of PND 21 was significantly increased, and the ovarian structure was damaged when exposed to BPA. In contrast, the mice with PND 45 did not show apparent ovarian lesions. On the other hand, granulosa cell apoptosis was detected in both PND 21 and PND 45 mice ovaries, and ERβ was increased under the influence of BPA. Transcriptomic analysis revealed BPA's significant impact on ribosomal gene expression, marked downregulation of Rpl21 and Rpsa, and upregulation of Rps2 in both age groups. These transcriptomic alterations were further corroborated by real-time PCR, highlighting a dose-dependent effect of BPA on Rps2. Our findings confirm BPA's detrimental effects on ovarian health, with more pronounced damage in younger mice, suggesting heightened vulnerability in this group. The study underscores ribosomes as critical targets in BPA-induced ovarian developmental disruptions. [ABSTRACT FROM AUTHOR]

The study proposes an active trailer steering control method for tractor semitrailers to promote the path tracking effect of the trailer portion as well as lateral stability during lane changing. Firstly, a simplified model of a tractor semitrailer is constructed, and the MAP map is formed based on the genetic algorithm for the identification of the key parameters, which improves the model's accuracy. Then the tractor and trailer's yaw rate and sideslip angle at CG are tracked as the control objective and the trailer angle distribution strategy is given. Then the LQR-based corner controller is designed to control the steering actuators of each axle of the trailer. Finally, the effectiveness of the designed control strategy is verified based on the Trucksim/Simulink joint simulation platform and the semi-physical HiL test platform. The simulation results show that the designed controller can effectively improve the path tracking effect of the tractor and the trailer, and at the same time, the lateral stability parameters of the tractor and the trailer are also significantly improved, which improves the driving stability of the tractor semitrailer. [ABSTRACT FROM AUTHOR]

We prove that the R-matrix and Drinfeld presentations of the Yangian double in type A are isomorphic. The central elements of the completed Yangian double in type A at the critical level are constructed. The images of these elements under a Harish-Chandra-type homomorphism are calculated by applying a version of the Poincaré-Birkhoff-Witt theorem for the R-matrix presentation. These images coincide with the eigenvalues of the central elements in the Wakimoto modules. [ABSTRACT FROM AUTHOR]

Motivation Large language models, trained on enormous corpora of biological sequences, are state-of-the-art for downstream genomic and proteomic tasks. Since the genome contains the information to encode all proteins, genomic language models (gLMs) hold the potential to make downstream predictions not only about DNA sequences, but also about proteins. However, the performance of gLMs on protein tasks remains unknown, due to few tasks pairing proteins with the coding DNA sequences (CDS) that can be processed by gLMs. Results In this work, we curated five such datasets and used them to evaluate the performance of gLMs and proteomic language models (pLMs). We show that gLMs are competitive and even outperform their pLMs counterparts on some tasks. The best performance was achieved using the retrieved CDS compared to sampling strategies. We found that training a joint genomic-proteomic model outperforms each individual approach, showing that they capture different but complementary sequence representations, as we demonstrate through model interpretation of their embeddings. Lastly, we explored different genomic tokenization schemes to improve downstream protein performance. We trained a new Nucleotide Transformer (50M) foundation model with 3mer tokenization that outperforms its 6mer counterpart on protein tasks while maintaining performance on genomics tasks. The application of gLMs to proteomics offers the potential to leverage rich CDS data, and in the spirit of the central dogma, the possibility of a unified and synergistic approach to genomics and proteomics. Availability and implementation We make our inference code, 3mer pre-trained model weights and datasets available. [ABSTRACT FROM AUTHOR]

Introduction: A comprehensive and global knowledge of protein target engagement is of vital importance for mechanistic studies and in drug development. Since its initial introduction, the cellular thermal shift assay (CETSA) has proven to be a reliable and flexible technique that can be widely applied to multiple contexts and has profound applications in facilitating the identification and assessment of protein target engagement. Areas covered: This review introduces the principle of CETSA, elaborates on western blot-based CETSA and MS-based thermal proteome profiling (TPP) as well as the major applications and prospects of these approaches. Expert opinion: CETSA primarily evaluates a given ligand binding to a particular target protein in cells and tissues with the protein thermal stabilities analyzed by western blot. When coupling mass spectrometry with CETSA, thermal proteome profiling allows simultaneous proteome-wide experiment that greatly increased the efficiency of target engagement evaluation, and serves as a promising strategy to identify protein targets and off-targets as well as protein-protein interactions to uncover the biological effects. The CETSA approaches have broad applications and potentials in drug development and clinical research. [ABSTRACT FROM AUTHOR]

Protein language models (PLMs) play a dominant role in protein representation learning. Most existing PLMs regard proteins as sequences of 20 natural amino acids. The problem with this representation method is that it simply divides the protein sequence into sequences of individual amino acids, ignoring the fact that certain residues often occur together. Therefore, it is inappropriate to view amino acids as isolated tokens. Instead, the PLMs should recognize the frequently occurring combinations of amino acids as a single token. In this study, we use the byte-pair-encoding algorithm and unigram to construct advanced residue vocabularies for protein sequence tokenization, and we have shown that PLMs pre-trained using these advanced vocabularies exhibit superior performance on downstream tasks when compared to those trained with simple vocabularies. Furthermore, we introduce PETA, a comprehensive benchmark for systematically evaluating PLMs. We find that vocabularies comprising 50 and 200 elements achieve optimal performance. Our code, model weights, and datasets are available at https://github.com/ginnm/ProteinPretraining. Scientific contribution: This study introduces advanced protein sequence tokenization analysis, leveraging the byte-pair-encoding algorithm and unigram. By recognizing frequently occurring combinations of amino acids as single tokens, our proposed method enhances the performance of PLMs on downstream tasks. Additionally, we present PETA, a new comprehensive benchmark for the systematic evaluation of PLMs, demonstrating that vocabularies of 50 and 200 elements offer optimal performance. [ABSTRACT FROM AUTHOR]