Relaxed Constraints Research Articles

Self-triggered fixed-time bipartite fault-tolerant consensus for nonlinear multiagent systems with function constraints on states

This article presents a self-triggered bipartite fault-tolerant consensus control scheme in a fixed-time stability sense for multiagent systems (MASs) with function constraints on states. Neural networks are introduced to identify unknown nonlinearities, thereby relaxing constraints on unknown functions. Then, based on time-varying barrier Lyapunov functions including time and previous states, all states of the considered MASs are constrained to given ranges. In addition, to improve the utilization of system transmission resources, a self-triggered control method in which the next triggering time can be computed according to the current information of the controller is proposed. By applying the Lyapunov theory, the designed self-triggered controller can ensure that all signals containing consensus tracking errors are fixed-time bounded under a given communication topology, and the Zeno phenomenon is successfully avoided. Finally, a practical example is provided to testify the feasibility of the developed control scheme.

Trajectory planning for satellite swarms with nonlinear terminal constraints using penalty concave relaxation

Convex programming (CP) is widely used in trajectory planning for space missions due to its high efficiency. Existing CP methods may not handle well with trajectory planning problem for satellite swarms involving multiple nonlinear terminal constraints, leading to solution chattering and initial infeasibility. To overcome this issue, this paper introduces a penalty concave relaxation (PCR) treatment to the conventional CP methods. First, the nonconvex terms in multiple nonlinear terminal constraints are equivalently concentrated into a unique equality constraint to reduce the number of relaxation variables. This equality constraint is then relaxed along the concave direction to guarantee the initial feasibility of the subsequent iterative solution process. Meanwhile, only one penalty coefficient is added on the objective. Finally, the relaxed concave constraint is linearized so that chattering can be avoided in an iterative strategy to solve the original swarm trajectory planning problem. Numerical examples are set up for two swarm trajectory planning missions with nonlinear terminal constraints. The performance of avoiding chattering and ensuring initial feasibility is verified.

An effective data placement strategy for IIoT applications

SummaryWith the rapid development of the Internet of things (IoT) and mobile communication technology, the amount of data related to industrial Internet of things (IIoT) applications has shown a trend of explosive growth, and hence edge‐cloud collaborative environment becomes one of the most popular paradigms to place the IIoT applications data. However, edge servers are often heterogeneous and capacity limited while having lower access delay, so there is a contradiction between capacity and latency while using edge storage. Additionally, when IIoT applications deployed crossing edge regions, the impact of data replication and data privacy should not be ignored. These factors often pose challenges to proposing an effective data placement strategy to take full advantage of edge storage. To address these challenges, an effective data placement strategy for IIoT applications is designed in this article. We first analyze the data access time and data placement cost in an edge‐cloud collaborative environment, with the consideration of data replication and data privacy. Then, we design a data placement strategy based on ‐constraint and Lagrangian relaxation, to reduce the data access time and meanwhile limit the data placement cost to an ideal level. As a result, our proposed data placement strategy can effectively reduce data access time and control data placement costs. Simulation and comparative analysis results have demonstrated the validity of our proposed strategy.

Body size evolution in otters distinguished from terrestrial mustelids.

Some taxa of mammals live in water, all of which evolved from land-dwelling ancestors. In the family Mustelidae (Mammalia: Carnivora), most species live on land, while otters, comprising the subfamily Lutrinae, inhabit aquatic environments, which include the almost exclusively aquatic sea otters (Enhydra lutris). Thus, the transition from a terrestrial to an aquatic lifestyle has occurred within this family. Despite potentially different selection pressures on body size in aquatic and terrestrial habitats, no divergence in the evolutionary pattern of body size between otters and other mustelids has previously been shown using models of trait evolution on a phylogeny. We applied models that explicitly incorporated lineage-specific directional selection to the evolution of body mass in living mustelids. Using a simulation-based likelihood and approximate Bayesian computation approach, we demonstrated lineage-specific directional selection for larger body mass in otters, which is distinct from other mustelids. There was no evidence of a difference between sea otters and other otters in the strength of directional selection for larger body mass. Additionally, our analyses supported no difference in the rate at which body mass evolves in both directions between otters and other mustelids. These findings suggest that the evolution of body mass in otters is associated with selective advantages of larger size rather than the relaxation of constraints on body size in aquatic habitats, like other aquatic mammals such as sirenians, cetaceans, and pinnipeds.

Signal enhancement and efficient DTW-based comparison for wearable gait recognition

The popularity of biometrics-based user identification has significantly increased over the last few years. User identification based on the face, fingerprints, and iris, usually achieves very high accuracy only in controlled setups and can be vulnerable to presentation attacks, spoofing, and forgeries. To overcome these issues, this work proposes a novel strategy based on a relatively less explored biometric trait, i.e., gait, collected by a smartphone accelerometer, which can be more robust to the attacks mentioned above. According to the wearable sensor-based gait recognition state-of-the-art, two main classes of approaches exist: 1) those based on machine and deep learning; 2) those exploiting hand-crafted features. While the former approaches can reach a higher accuracy, they suffer from problems like, e.g., performing poorly outside the training data, i.e., lack of generalizability. This paper proposes an algorithm based on hand-crafted features for gait recognition that can outperform the existing machine and deep learning approaches. It leverages a modified Majority Voting scheme applied to Fast Window Dynamic Time Warping, a modified version of the Dynamic Time Warping (DTW) algorithm with relaxed constraints and majority voting, to recognize gait patterns. We tested our approach named MV-FWDTW on the ZJU-gaitacc, one of the most extensive datasets for the number of subjects, but especially for the number of walks per subject and walk lengths. Results set a new state-of-the-art gait recognition rate of 98.82% in a cross-session experimental setup. We also confirm the quality of the proposed method using a subset of the OU-ISIR dataset, another large state-of-the-art benchmark with more subjects but much shorter walk signals.

Selective tightening algorithm for the optimization of pipeline network designs in the energy industry

Energy industries face the challenge on how to design networks to gather flows from unconventional assets due to the relative short lifetime of the wells. The optimal design of the network of pipelines and processing facilities is a challenging problem from both combinatorial and nonlinear viewpoints. To date, real instances of this problem cannot be solved to global optimality unless simplifying assumptions are made. We propose a systematic algorithm to address the optimal planning of gathering networks in a multiperiod horizon. It relies on the strategic selection of links on which fluid-dynamic equations are imposed. By relaxing constraints, the resulting mixed-integer programming models are still complex from the combinatorial standpoint, but they can be solved in reasonable computational times. The algorithm progressively adds constraints to the potential arcs, seeking for the global optimal solution by selectively tightening relaxations. Results show that computational times can be reduced by two orders of magnitude.

Reliability-Aware Task Processing and Offloading for Data-Intensive Applications in Edge computing

With the growing popularity of mobile edge computing (MEC), a number of data-intensive applications have been deployed. Quality of Service (QoS), as one of the most important requirements in MEC, has attracted significant attention of both academia and industry. There are two challenges for ensuring the Qos of the data-intensive services. Firstly, besides performance, reliability is another important concern especially for some critical applications, which remains unexplored. Secondly, data compression has to be involved for reducing the heavy workload of wireless communications at the edge of the network. To overcome these challenges, this paper jointly studies the reliability-aware data compression and task offloading for data-intensive applications in MEC. Markov models are constructed to capture the dynamics of the state transitions of MEC systems, and quantitative analyses are conducted for performance and reliability evaluation. For fully taking advantages of data compression in QoS guarantee, we formulate an optimization problem with the objective of minimizing latency while satisfying constraints on reliability and energy consumption. After describing the NP-Hardness of the problem, we apply the techniques of problem linearization and constraint relaxation, transform the original problem into a convex optimization problem. Then, the problem can be solved in a parallel way by introducing the Alternating Direction Multiplier Method (ADMM), and a distributed Reliability-aware Task Processing and Offloading (RTPO) algorithm is presented. Finally, extensive simulation experiments are conducted to validate the efficacy of our approach, the experimental results illustrate the superiority of our approach over both baseline and state-of-the-art algorithm.

Robust Secure Transmission for Active RIS Enabled Symbiotic Radio Multicast Communications

In this paper, we propose a robust secure transmission scheme for an active reconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system in the presence of multiple eavesdroppers (Eves). In the considered system, the active RIS is adopted to enable the secure transmission of primary signals from the primary transmitter to multiple primary users in a multicasting manner, and simultaneously achieve its own information delivery to the secondary user by riding over the primary signals. Taking into account the imperfect channel state information (CSI) related with Eves, we formulate the system power consumption minimization problem by optimizing the transmit beamforming and reflection beamforming for the bounded and statistical CSI error models, taking the worst-case SNR constraints and the SNR outage probability constraints at the Eves into considerations, respectively. Specifically, the S-Procedure and the Bernstein-Type Inequality are implemented to approximately transform the worst-case SNR and the SNR outage probability constraints into tractable forms, respectively. After that, the formulated problems can be solved by the proposed alternating optimization (AO) algorithm with the semi-definite relaxation and sequential rank-one constraint relaxation techniques. Numerical results show that the proposed active RIS scheme can reduce up to 27.0% system power consumption compared to the passive RIS.

Exploring the endogenous effects among car dependency, work arrangement choice, and daily travel using the 2017 NHTS data

The paper presents an effort in investigating the cause-effect relationships among telecommuting, car dependency, and trip making behavior. Data from the 2017 National Household Travel Survey (NHTS) was used to develop a structural equations model (with latent constructs) to examine the endogenous effects between the decision to telework, the degree of car dependency, and the number of daily trips. Using confirmatory factor analysis, car dependency was measured by vehicle ownership, annual mileage, and car use frequency. The model provided interesting insights. Car dependency had a negative (both direct and total) impact on telework, an inference that confirms the role of car dependency as a resistant factor against alternative work arrangements and potentially any other new tech-based policies. In the opposite direction and surprisingly, telework encouraged car dependency, which might indicate that teleworkers tended to utilize the relaxed temporal-spatial constraints for non-work trips, and they were unlikely to give up private vehicle ownership simply because of their option to telecommute. Second, number of daily trips tended to increase the probability to telework, confirming the positive endogenous role of daily activity patterns on work arrangement decisions in a daily framework. Lastly, the significant negative impact of telework on daily trips was positively mediated through car dependency, leading to a smaller negative total impact on daily trips. Our study confirms that the association between telework and trip generation is quite a complex and multi-faceted relationship, leaving the argument regarding whether or not telework increases the number of daily trips as a debatable topic that calls for further exploration.

A parametric study into the influence of Taylor-type scale-bridging artifacts on accuracy of multi-level crystal plasticity finite element models for Mg alloys

Meshing grain structures explicitly to incorporate microstructure dependent material behavior in modeling tools for metal forming processes and structural components is unfeasible. Grain-to-polycrystal meso-level homogenization theories are employed to embed polycrystal plasticity constitutive laws in finite element (FE) frameworks, which hence relate the meso-scale to the macro-scale response. A Taylor-type polycrystal plasticity (T-CP) theory is often used at the meso-scale within FE frameworks (T-CPFE) owing to its simplicity and computational efficiency. The theory relies on the iso-strain constraint imposed over constituent grains at each integration point. The constraint can be relaxed by spreading orientation distributions over finite elements in a mesh. This work seeks to establish an optimal number of crystal orientations to spread over integration points for accurate modeling of Mg alloys. Quasi-static and high strain-rates simulations of tension, compression, simple-shear, and plane strain deformation conditions are performed and post-processed to reveal the differences in predicted mechanical fields between T-CPFE and an explicit polycrystalline grain microstructure of an AZ31 Mg alloy. Moreover, several flow stress curves of the alloy are simulated and compared with measured data. A range of meshes with variable degree of relaxed constraints at integration points are suitably designed and used in the simulations. The performance of the six crystals per integration point is established to be an optimum in smoothing local deformation while allowing heterogenous deformation over the mesh. As such, the relaxed Taylor homogenization can provide tractable part level simulations of Mg alloys.

Mitochondrial phylogenomics of bumblebees, Bombus (Hymenoptera: Apidae): a tale of structural variation, shifts in selection constraints, and tree discordance

Abstract The mitochondrial DNA (mtDNA) of bumblebees (Bombus) has been widely used for phylogenetic studies, but its evolution is still underexplored. Here we report a comprehensive analysis of 60 bumblebee mitogenomes, including 40 newly assembled ones, to investigate bumblebee mtDNA structure, composition, and informativeness under a phylogenetic framework. Our mtDNA dataset supports the monophyly of Bombus and its subgenera, although we found a high degree of tree discordance in deeper nodes when using different inference methods or matrix composition. Concerning mitogenome structure, our results show that tRNA genes were often rearranged, with unique rearrangements indicating shared ancestry across bumblebee subgenera, illustrating their potential for subgeneric classification. Our results also challenge the notion that faster evolving mtDNA exhibits higher gene rearrangement rates. Finally, we explicitly assessed shifts in selection constraints of mtDNA genes in obligate social parasites of subgenus Psithyrus and found that their mtDNA evolved under relaxed selective constraints. Our findings show the utility of mtDNA in providing insights into bumblebee phylogenetics, evolution, and genome trait diversification. We also highlight the potential for comparative mitogenomics to uncover previously unknown aspects of bumblebee evolution, offering exciting opportunities for future research in this field.

Over-Stoichiometric Metastabilization of Cation-Disordered Rock Salts.

Cation-disordered rock salts (DRXs) are well known for their potential to realize the goal of achieving scalable Ni- and Co-free high-energy-density Li-ion batteries. Unlike in most cathode materials, the disordered cation distribution may lead to more factors that control the electrochemistry of DRXs. An important variable that is not emphasized by research community is regarding whether a DRX exists in a more thermodynamically stable form or a more metastable form. Moreover, within the scope of metastable DRXs, over-stoichiometric DRXs, which allow relaxation of the site balance constraint of a rock salt structure, are particularly underexplored. In this work, these findings are reported in locating a generally applicable approach to "metastabilize" thermodynamically stable Mn-based DRXs to metastable ones by introducing Li over-stoichiometry. The over-stoichiometric metastabilization greatly stimulates more redox activities, enables better reversibility of Li deintercalation/intercalation, and changes the energy storage mechanism. The metastabilized DRXs can be transformed back to the thermodynamically stable form, which also reverts the electrochemical properties, further contrasting the two categories of DRXs. This work enriches the structural and compositional space of DRX families and adds new pathways for rationally tuning the properties of DRX cathodes.

CTNI-01. LONG-TERM RESULTS FROM A PHASE 1 TRIAL OF SPINE SBRT IN INOPERABLE PATIENTS WITH CORD COMPRESSION

Abstract PURPOSE/OBJECTIVE We seek to establish the feasibility of using spine stereotactic radiosurgery (SSRS) allowing for spinal cord dose constraint relaxation as the primary management of metastatic epidural spinal cord compression (MESCC) in inoperable patients monitoring for radiation myelopathy (RM) and radiographic local control (LC). MATERIAL/METHODS Patients with radiation naïve MESCC were enrolled on this prospective Phase 1 trial. Single fraction SSRS was delivered to a dose of 18 or 24 Gy. Spinal cord constraint relaxation was performed in sequential cohorts from an initial allowable Dmax cohort of 10 Gy up to 16 Gy only if tumor progression occurred without RM. RESULTS Thirty two patients enrolled on the trial of which 4, 12, 8 and 8 were in the 10 Gy, 12 Gy, 14 Gy and 16 Gy cord Dmax cohorts, respectively. At baseline, there were 10 sites with MESCC Grade 1B, 10 sites with Grade 1C, 9 sites with Grade 2, 2 sites with Grade 1A, and 1 site with Grade 3 disease. Of the 28 evaluable patients, the median overall survival was 32.3 months (range 5.8-122.6 mo). The 1-year and 5-year LC was 84.5% and 79.5%. The 2-year LC did not statistically differ between the 14-16 Gy cord Dmax combined cohorts and the 10-12 Gy cord Dmax combined cohorts (92.9% vs. 62.9%, p = 0.15). With a median clinical follow-up of 22.7 months (range 3-122.3 mo), there were no cases of RM including in the 13 patients who survived at least 3 years. In the cohort receiving a cord Dmax of 16 Gy, there were no cases of RM with a median follow-up of 18.6 mo (range 9.0-97.1 mo). CONCLUSION With long-term follow-up, these data demonstrate that SSRS is a safe and effective tool in patients with MESCC. Cord constraint relaxation may be considered in inoperable patients with MESCC.

Bi-directional search based on constraint relaxation for constrained multi-objective optimization problems with large infeasible regions

How to balance the satisfaction of constraints and the optimization of objective functions is one of the key issues to solve constrained multi-objective optimization problems (CMOPs), especially when the constraints are complex. Although many algorithms have been designed to handle this, most of them are still unable to effectively handle CMOPs with complex constraints. Based on the above issue, this paper proposes a framework for bi-directional search, which evolves two populations (P1 and P2). P1 aims to search the constrained Pareto front (CPF) from the infeasible side of the objective space, and P2 from the feasible side, aiming to achieve a more efficient and comprehensive bi-directional search for the CPF. To ensure the diversity, we adopt a preferred weight vector selection strategy to choose potential mating parents, which improves the search capability for the marginal CPF. Furthermore, to coordinate the interaction between the two populations, we propose an environmental selection strategy to select the offspring generated by P1 and P2 under the same weight vector with the better fitness to update the populations respectively, and the fitness is evaluated based on the different constraint relaxations of the two populations, to update them respectively. Extensive experiments indicate that our proposed algorithm has significantly better results or was at least competitive when compared to eight state-of-the-art methods.

Walking back from the edge: thresholds of change reveal options for adaptation to water scarcity under climate change in the Murray–Darling Basin, Australia

Climate change has increased the variability of river inflows in the Murray–Darling Basin, threatening the viability of irrigated agriculture, food processing industries and ecological condition of wetlands. With increasing water scarcity, decision-makers and communities face heightened contestation over scarce water resources and trade-offs and adaptation have become increasingly necessary. We used a social-ecological systems approach to identify thresholds of change in the Goulburn–Broken Catchment, a major food-producing region, to reveal options for adaptation to climate change. We developed systems models whereby feedbacks are identified between sub-systems of cultural paradigms, policies, human well-being and environmental condition. Models were constructed using data from semi-structured interviews with managers and decision-makers, industry reports and the scientific literature. We found environmental thresholds are fixed, but whether they are exceeded is socially determined. Environmental condition can be maintained by relaxing constraints on volumes of water released into the highly regulated river system and easing rules on the distribution of water among users in the dairy and horticulture industries. Socio-economic thresholds were more flexible. Industries have adapted to water scarcity through irrigation efficiency measures, inter-industry relationships for water-sharing and feed substitutes in dairy production. However, industry interdependence indicates potential for maladaption, whereas investment in adaptation and diversification offers more sustainable options. Current policy and management disconnects between water for the environment and water for food production reveal opportunities for co-benefits between environmental and socio-economic domains. Realising these benefits requires a systemic, inclusive adaptation pathways approach to design and implement options for change.

A Neanderthal/Denisovan GLI3 variant contributes to anatomical variations in mice.

Changes in genomic structures underlie phenotypic diversification in organisms. Amino acid-changing mutations affect pleiotropic functions of proteins, although little is known about how mutated proteins are adapted in existing developmental programs. Here we investigate the biological effects of a variant of the GLI3 transcription factor (GLI3R1537C) carried in Neanderthals and Denisovans, which are extinct hominins close to modern humans. R1537C does not compromise protein stability or GLI3 activator-dependent transcriptional activities. In contrast, R1537C affects the regulation of downstream target genes associated with developmental processes. Furthermore, genome-edited mice carrying the Neanderthal/Denisovan GLI3 mutation exhibited various alterations in skeletal morphology. Our data suggest that an extinct hominin-type GLI3 contributes to species-specific anatomical variations, which were tolerated by relaxed constraint in developmental programs during human evolution.

Disclosure Tone and Short-Selling Pressure: Evidence from Regulation-SHO

Managers use disclosure tone as a strategic tool to manage investors’ expectations and demand for information. I provide evidence that investors’ actions can, in turn, exercise a disciplining effect on tone management. Using exogenous relaxation in the short-selling constraints from Regulation-SHO and employing the difference-in-differences design on a propensity-score matched sample, I find that short-selling pressure reduces tone management. Greater short- selling pressure results in less optimism in tone unrelated to fundamentals, and in disclosures about the future rather than the past. Moreover, this reduction in tone management is stronger for firms with higher short-selling constraints pre-Regulation-SHO and for those with overoptimistic and overconfident managers.

Influence of water saturation on interlayer properties of HDTMA-, HDTMP-, and HDPy-modified montmorillonite organoclays

Surfactant-modified clay minerals, organoclays, are well-studied and used commercially for removing contaminants from water. Nevertheless, dry organoclay properties are typically used to understand and predict contaminant sorption. In this work, the effects of water saturation on two properties important to contaminant sorption were examined: organoclay interlayer space and surfactant alkyl tail conformational ordering. Montmorillonite was modified to 0.25–3.0 CEC using three surfactants: hexadecyltrimethylammonium (HDTMA), hexadecylpyridinium (HDPy), and hexadecyltrimethylphosphonium (HDTMP). At low surfactant-loadings (< 1 CEC and < 15% fOC), water saturation expanded the maximum organoclay interlayer by 4–8 Å, depending on the surfactant and its loading but had little effect on surfactant tail conformational ordering. At low surfactant loadings, water saturation likely promotes contaminant sorption relative to expectations based on dry organoclay properties, particularly for larger contaminants, due to a relaxation of the physical constraints of the interlayer. At higher surfactant loadings, HDTMA and HDTMP organoclays showed relatively small effects of water saturation, but effects were significant for HDPy organoclays. The maximum interlayer space of the HDPy organoclay at 20.7% fOC expanded 3-fold (+22.3 Å) upon hydration, which is attributed to a substantial rearrangement of the pyridinium headgroup. All HDPy organoclays with fOC > 20% experienced a notable increase in the alkyl tail conformational ordering upon hydration, becoming fully solid-like, even as negligible interlayer expansion occurred at the highest loadings. At high HDPy-loading water saturation would likely restrict sorption of contaminants relative to what might be expected based on dry properties, due to the energetic barrier of cavity formation in the more solid-like interlayer phase. This work provides evidence from three types of organoclays that water-saturated organoclay properties can differ substantially from those of dry organoclays. Characterization of organoclays under water-saturated conditions that are relevant to contaminant sorption will facilitate our understanding and improvement of organoclay performance.

H∞ filtering for discrete-time cyclic switched systems: Relaxed cycle-dependent persistent dwell-time constraints with averaging treatment

This note investigates the H∞ filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and l2-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and H∞ noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.

Superposition of modulated nonlinear waves in inhomogeneous systems with negative coherent coupling

The superimposed wave solutions of the variable coefficient nonlinear Schrödinger equations with negative coherent coupling are derived under a more relaxed constraint condition than those in previous literatures. For the benefit of the more relaxed constraint, the dispersion, nonlinearity, and gain/loss can be designed freely, and the obtained solutions can describe the nonlinear waves in general inhomogeneous optical fiber systems. The obtained solutions with two free phase parameters can be deemed to be the superposition of the typical simple modulated solutions, and the arbitrary of the optical parameters and the free phase parameters be expected to give the rise of abundant forms of modulation functions, that leads to the diverse characteristics of superimposed waves. Take the kink dispersion fiber systems with constant gain/loss and trigonometric gain/loss as examples, rich dynamics of the superimposed waves are displayed. By changing the gain/loss, the physical features of superimposed waves, such as the amplitudes of solitons and Kuznetsov-Ma breathers, the widths of solitons, the distances between Kuznetsov-Ma breathers, and the backgrounds of Akhmediev breathers and rogue waves can be controlled. The interaction of solitons or Kuznetsov-Ma breathers, and the number of the rogue waves or Akhmediev breathers can also be manipulated by selecting appropriate value of gain/loss. The results presented here may be useful to explore the diverse dynamics of superimposed waves and prove significance for the control of nonlinear waves in weakly birefringent fibers.