Predictions Of Theory Research Articles

Inverse Differential Quadrature Based Model for Static Behaviour of Variable Stiffness Curved Composite Beams

Recent advancements in fibre placement technologies have expanded the potential applications of variable stiffness curved composite beams in industries such as aerospace, automotive, and naval engineering. Accurate solution techniques for examining these beams, especially those composed of advanced composite materials, are indispensable. In view of this demand, this study proposes a new high-order computational tool that combines the higher-order accuracy of the emerging inverse differential quadrature method (iDQM) and the simple kinematics of the Timoshenko beam theory for efficient and accurate prediction of the static behaviour of both constant stiffness and variable stiffness curved beam structures. This novel application of iDQM to curved beam analysis is leveraged upon its excellent potential to mitigate differentiation-induced errors by using the so-called indirect approximation strategy. Simple procedures for implementing different orders of iDQM models are presented to analyse curved beam problems, and are independently benchmarked against closed-form Navier's solutions, as well as numerical solutions obtained through the differential quadrature method (DQM) and finite element method (FEM), demonstrating excellent spectral accuracy. Furthermore, the iDQM scheme offers outstanding potential in recovering transverse shear stress, achieving superior accuracy over lower-order FEM in approximating higher-order derivatives. Remarkably, iDQM predictions for variable stiffness curved beams exhibit satisfactory agreement with the Strong Unified Formulation, achieving over 98% computational efficiency. Finally, convergence analysis of iDQM solutions reveal up to three orders of improved accuracy and faster convergence rates compared to the DQM, constituting a new benchmark for curved beam analysis.

Hybrid model predictive control for vehicle trajectory tracking with integrated attitude adjustment

This paper presents a vehicle trajectory tracking method that integrates attitude adjustment. The method utilizes the asymmetric adjustment of the damping of the adjustable damping shock absorber to lift the left and right vehicle body and carry out the attitude adjustment of the vehicle. Additionally, it actively tilts toward the inside of the curve during turning. In order to address the nonlinear constraints of damping asymmetry regulation and the mixed logic relationship between suspension asymmetry damping switching and left and right body lifting during body attitude regulation, a mixed logic dynamic system (MLD) for vehicle attitude adjustment is established. Subsequently, the vehicle trajectory tracking controller is designed using the hybrid model predictive control theory (HMPC), which integrates active steering control and attitude adjustment. The optimal control problem of hybrid systems is transformed into a hybrid integer quadratic programming problem and solved through finite time domain rolling optimization. The effectiveness of the proposed integrated controller is confirmed through Simulink simulation. Compared with pure tracking control and roll tracking control with zero roll angle as the control target, this controller demonstrates its ability to effectively track the reference trajectory and enhance the vehicle’s dynamic performance.

Design, synthesis, and bioevaluation of novel unsaturated cyanoacetamide derivatives: In vitro and in silico exploration

In this study, we synthesized novel α,β-unsaturated 2-cyanoacetamide derivatives (1–5) using microwave-assisted Knoevenagel condensation. Characterization of these compounds was carried out using FTIR and 1H NMR spectroscopy. We then evaluated their in vitro antibacterial activity against both gram-positive and gram-negative pathogenic bacteria. Additionally, we employed in silico methods, including ADMET prediction and density functional theory (DFT) calculations of molecular orbital properties, to investigate these cyanoacetamide derivatives (1–5). Molecular docking was used to assess the binding interactions of these derivatives (1–5) with seven target proteins (5MM8, 4NZZ, 7FEQ, 5NIJ, ITM2, 6SE1, and 5GVZ) and compared them to the reference standard tyrphostin AG99. Notably, derivative 5 exhibited the most favorable binding affinity, with a binding energy of -7.7 kcal mol−1 when interacting with the staphylococcus aureus (PDB:5MM8), while also meeting all drug-likeness criteria. Additionally, molecular dynamics simulations were carried out to evaluate the stability of the interaction between the protein and ligand, utilizing parameters such as Root-Mean-Square Deviation (RMSD), Root-Mean-Square Fluctuation (RMSF), Radius of Gyration (Rg), and Principal Component Analysis (PCA). A 50 nanosecond molecular dynamics (MD) simulation was performed to investigate stability further, incorporating RMSD and RMSF analyses on compound 5 within the active binding site of the modeled protein across different temperatures (300, 305, 310, and 320 K). Among these temperatures, compound 5 exhibited an RMSD value ranging from approximately 0.2 to 0.3 nm at 310 K (body temperature) with the 5MM8 target, which differed from the other temperature conditions. The in silico results suggest that compound 5 maintained significant conformational stability throughout the 50 ns simulation period. It is consistent with its low docking energy and in vitro findings concerning α,β-unsaturated cyanoacetamides.Key insights from this study include:•The creation of innovative α,β-unsaturated 2-cyanoacetamide derivatives (1–5) employing cost-effective, licensed, versatile, and efficient software for both in silico and in vitro assessment of antibacterial activity.•Utilization of FTIR and NMR techniques for characterizing compounds 1–5.

Pregnancy is linked to faster epigenetic aging in young women

A central prediction of evolutionary theory is that energy invested into reproduction comes at the expense of somatic maintenance and repair, accelerating biological aging. Supporting this prediction are findings that high fertility among women predicts shorter lifespan and poorer health later in life. However, biological aging is thought to begin before age-related health declines, limiting the applicability of morbidity and mortality for studying the aging process earlier in life. Here, we examine the relationship between reproductive history and biological aging in a sample of young (20 to 22yo) men and women from the Cebu Longitudinal Health and Nutrition Survey, located in the Philippines (n = 1,735). We quantify biological aging using six measures, collectively known as epigenetic clocks, reflecting various facets of cellular aging, health, and mortality risk. In a subset of women, we test whether longitudinal changes in gravidity between young and early-middle adulthood (25 to 31yo) are associated with changes in epigenetic aging during that time. Cross-sectionally, gravidity was associated with all six measures of accelerated epigenetic aging in women (n = 825). Furthermore, longitudinal increases in gravidity were linked to accelerated epigenetic aging in two epigenetic clocks (n = 331). In contrast, the number of pregnancies a man reported fathering was not associated with epigenetic aging among same-aged cohort men (n = 910). These effects were robust to socioecological, environmental, and immunological factors, consistent with the hypothesis that pregnancy accelerates biological aging and that these effects can be detected in young women in a high-fertility context.

Improving the density functional theory prediction accuracy for elastic moduli and thermal expansion of MoAlB, Fe2AlB2, and Mn2AlB2

AbstractThe elastic moduli and thermal expansion of MoAlB, Fe2AlB2, and Mn2AlB2 are investigated by first‐principles calculations, in particular to improve the density functional theory (DFT) prediction accuracy after clarifying the critical role of their lattice constants. By calculating the lattice constants and elastic moduli using the typical exchange‐correlation functionals, the observed positive correlation between the calculation errors of elastic moduli and those of cell volumes suggests a method to significantly improve the calculation accuracy for elastic moduli using the experimental cell volume to correct the input model (volume correction method), resulting in satisfactory results. Furthermore, a two‐step strategy is proposed for the precise high‐temperature elastic moduli with the help of quasi‐harmonic approximation for the most accurate high‐temperature cell volume using an exchange‐correlation functional in the first step, and another one used in the volume correction method in the second step. Similarly, the calculation accuracy of thermal expansion also heavily depends on that of cell volumes and configurations, where their thermal expansion is estimated with great accuracy by using the exchange‐correlation functional that well reproduces the lattice constants.

Investigating change in network structure of eating disorder symptoms after delivery of a smartphone app-based intervention.

Eating disorder (ED) research has embraced a network perspective of psychopathology, which proposes that psychiatric disorders can be conceptualized as a complex system of interacting symptoms. However, existing intervention studies using the network perspective have failed to find that symptom reductions coincide with reductions in strength of associations among these symptoms. We propose that this may reflect failure of alignment between network theory and study design and analysis. We offer hypotheses for specific symptom associations expected to be disrupted by an app-based intervention, and test sensitivity of a range of statistical metrics for identifying this intervention-induced disruption. Data were analyzed from individuals with recurrent binge eating who participated in a randomized controlled trial of a cognitive-behavioral smartphone application. Participants were categorized into one of three groups: waitlist (n = 155), intervention responder (n = 49), and intervention non-responder (n = 77). Several statistical tests (bivariate associations, network-derived strength statistics, network invariance tests) were compared in ability to identify change in network structure. Hypothesized disruption to specific symptom associations was observed through change in bivariate correlations from baseline to post-intervention among the responder group but were not evident from symptom and whole-of-network based network analysis statistics. Effects were masked when the intervention group was assessed together, ignoring heterogeneity in treatment responsiveness. Findings are consistent with our contention that study design and analytic approach influence the ability to test network theory predictions with fidelity. We conclude by offering key recommendations for future network theory-driven interventional studies.

Molecular simulation-guided and physics-informed constitutive modeling of highly stretchable hydrogels with dynamic ionic bonds

Adaptive polymers are being designed with dynamic molecular bonds or chain interactions to respond with external stimuli with unparalleled mechanical properties and multifunctionality. An elegant example is to substantially enhance the stretchability and toughness of hydrogels through the use of ionic bond interactions. To assist the materials design and applications, a predictive theory is in high demand. However, existing multi-scale mechanics models often rely on empirical assumptions and relationships derived from polymer chemistry or physics to describe the evolution of microscale details under external stimuli, which are challenging to be validated experimentally. This study introduces a new methodology to develop constitutive theories for stretchable hydrogels based on insights garnered from molecular dynamics (MD) simulations. The continuum-level viscoelastic theory establishes the thermodynamics framework for stress-strain relationships, while MD simulations inform the evolution mechanisms of microscale bond interactions and network rearrangements, such as the bond distance and network relaxation time. These insights are then properly formulated based on polymer physics principles and fed into the continuum-level model. The resulting constitutive theory closely captures the stress responses at various loading conditions observed in experiments, as well as the microscale system volume and bond distance uncovered in MD simulations. Parametric studies are conducted to investigate the influences of various loading and material parameters on the mechanical properties of the materials, including loading rates, network crosslinking density, maximum strain, and bonding strength. Overall, the study establishes the connection between microscale network structure and mechanical responses of stretchable hydrogels with dynamic ionic bonds. It also offers practical guidance for optimizing material structures and loading conditions to enhance energy absorption and dissipation capabilities. The modeling approach can be extended to the study of other adaptive polymers with different dynamic bonds to create more precise and physically meaningful constitutive models.

Theories of Uncertainty Communication: An Interdisciplinary Literature Review

This systematic literature review presents an interdisciplinary overview of theories tested in experiments on the effects of communicating uncertainty. Using a machine learning-aided pipeline, we selected and manually coded 413 experimental studies. We discuss core assumptions and predictions of the main theories of uncertainty communication. Most normative theorizing (e.g., Bayesianism, Expected Utility Theory) is rooted in Probability Theory, which is only suitable for addressing shallow and medium uncertainty. This explains the underrepresentation of experimental research into deep uncertainty communication. To foster a more comprehensive understanding of uncertainty communication effects, we identify research questions and theories deserving greater attention.

Quest for the golden ratio universality class.

Using mode-coupling theory, the conditions for all allowed dynamical universality classes for the conserved modes in one-dimensional driven systems are presented in closed form as a function of the stationary currents and their derivatives. With an eye on the search for the golden ratio universality class, the existence of some families of microscopic models is ruled out a priori by using an Onsager-type macroscopic current symmetry. In particular, if the currents are symmetric or antisymmetric under the interchange of the conserved densities, then at equal mean densities the golden modes can only appear in the antisymmetric case and if the conserved quantities are correlated, but not in the symmetric case where at equal densities one mode is always diffusive and the second may be either Kardar-Parisi-Zhang (KPZ), modified KPZ, 3/2-Lévy, or also diffusive. We also show that the predictions of mode-coupling theory for a noisy chain of harmonic oscillators are exact.

Evaluation of the helicoidal surface theory for the noise prediction of small UAS propellers

Evaluation of the helicoidal surface theory for the noise prediction of small UAS propellers

Dynamic screening by plasticity in amorphous solids.

In recent work it was shown that elasticity theory can break down in amorphous solids subjected to nonuniform static loads. The elastic fields are screened by geometric dipoles; these stem from gradients of the quadrupole field associated with plastic responses. Here we study the dynamical responses induced by oscillatory loads. The required modification to classical elasticity is described. Exact solutions for the displacement field in circular geometry are presented, demonstrating that dipole screening results in essential departures from the expected predictions of classical elasticity theory. Numerical simulations are conducted to validate the theoretical predictions and to delineate their range of validity.

The electrophysiology of lexical prediction of emoji and text

As emoji often appear naturally alongside text in utterances, they provide a way to study how prediction unfolds in multimodal sentences in direct comparison to unimodal sentences. In this experiment, participants (N = 40) read sentences in which the sentence-final noun appeared in either word form or emoji form, a between-subjects manipulation. The experiment featured both high constraint sentences and low constraint sentences to examine how the lexical processing of emoji interacts with prediction processes in sentence comprehension. Two well-established ERP components linked to lexical processing and prediction – the N400 and the Late Frontal Positivity – are investigated for sentence-final words and emoji to assess whether, to what extent, and in what linguistic contexts emoji are processed like words. Results indicate that the expected effects, namely an N400 effect to an implausible lexical item compared to a plausible one and an LFP effect to an unexpected lexical item compared to an expected one, emerged for both words and emoji. This paper discusses the similarities and differences between the stimulus types and constraint conditions, contextualized within theories of linguistic prediction, ERP components, and a multimodal lexicon.

Modification of extended Oxley’s predictive machining theory and determination of Johnson-Cook material model constants by inverse approach

The Johnson-Cook (J-C) flow stress model, renowned for its consideration of the combined effect of strain, strain-rate, and temperature on material property, forms the cornerstone of this research. Its simplicity and applicability in numerical simulation render it widely popular. The study addresses two primary objectives: first, to modify extended Oxley’s predictive machining theory by eliminating the iterative loop for calculating the tool-chip interface temperature, and second, to utilize an inverse approach for determining J-C material model constants specific to medium carbon steel. The modified approach successfully eliminates the iterative loop, thereby streamlining the determination process and effectively reducing calculation time by 25%–40%, thereby enhancing overall efficiency. Concurrently, the study employs an inverse approach to accurately determine the J-C constants (A, B, n, C, and m). Notably, the research avoids the need for expensive and time-consuming Split Hopkinson Pressure Bar (SHPB) tests, instead opting for low-cost axial tensile tests and numerical optimization techniques to obtain the J-C constants. Thus, this study provides a practical method for determining J-C constants, pivotal for accurate material representation in numerical simulations and metal cutting applications. Standard materials and machines are employed, ensuring ease of understanding for a wider audience. The predicted values for the J-C constants are in proximity to the experimental values obtained by using SHPB test. Validated findings, achieved with precision under specified metal cutting conditions, highlight the effectiveness and applicability of the proposed approach, providing valuable insights for optimizing machining processes and improving efficiency.

The object of jurisprudence

ABSTRACT Here I distinguish two things jurisprudence might take itself to explain. A theory of law can be either concept-first or practice-first. Concept-first theories investigate the concept we implicitly deploy to label some things as law and not others. Practice-first theories investigate directly, and uncover interesting features of, a particular social practice. That practice could be, for instance, the practice of lawyers and officials which prevails in the United States. I identify Hershovitz's Law Is a Moral Practice with a practice-first approach. Then I elaborate on the distinction and show that a practice-first approach is more defensible than many assume. Finally, I argue a practice-first approach rules out predictive theories of law.

A clinical decision support system using rough set theory and machine learning for disease prediction

ObjectiveTechnological advances have led to drastic changes in daily life, and particularly healthcare, while traditional diagnosis methods are being replaced by technology-oriented models and paper-based patient healthcare records with digital files. Using the latest technology and data mining techniques, we aimed to develop an automated clinical decision support system (CDSS), to improve patient prognoses and healthcare delivery. Our proposed approach placed a strong emphasis on improvements that meet patient, parent, and physician expectations. We developed a flexible framework to identify hepatitis, dermatological conditions, hepatic disease, and autism in adults and provide results to patients as recommendations. The novelty of this CDSS lies in its integration of rough set theory (RST) and machine learning (ML) techniques to improve clinical decision-making accuracy and effectiveness. MethodsData were collected through various web-based resources. Standard preprocessing techniques were applied to encode categorical features, conduct min-max scaling, and remove null and duplicate entries. The most prevalent feature in the class and standard deviation were used to fill missing categorical and continuous feature values, respectively. A rough set approach was applied as feature selection, to remove highly redundant and irrelevant elements. Then, various ML techniques, including K nearest neighbors (KNN), linear support vector machine (LSVM), radial basis function support vector machine (RBF SVM), decision tree (DT), random forest (RF), and Naive Bayes (NB), were employed to analyze four publicly available benchmark medical datasets of different types from the UCI repository and Kaggle. The model was implemented in Python, and various validity metrics, including precision, recall, F1-score, and root mean square error (RMSE), applied to measure its performance. ResultsFeatures were selected using an RST approach and examined by RF analysis and important features of hepatitis, dermatology conditions, hepatic disease, and autism determined by RST and RF exhibited 92.85 %, 90.90 %, 100 %, and 80 % similarity, respectively. Selected features were stored as electronic health records and various ML classifiers, such as KNN, LSVM, RBF SVM, DT, RF, and NB, applied to classify patients with hepatitis, dermatology conditions, hepatic disease, and autism. In the last phase, the performance of proposed classifiers was compared with that of existing state-of-the-art methods, using various validity measures. RF was found to be the best approach for adult screening of: hepatitis with accuracy 88.66 %, precision 74.46 %, recall 75.17 %, F1-score 74.81 %, and RMSE value 0.244; dermatology conditions with accuracy 97.29 %, precision 96.96 %, recall 96.96 %, F1-score 96.96 %, and RMSE value, 0.173; hepatic disease, with accuracy 91.58 %, precision 81.76 %, recall 81.82 %, F1-Score 81.79 %, and RMSE value 0.193; and autism, with accuracy 100 %, precision 100 %, recall 100 %, F1-score 100 %, and RMSE value 0.064. ConclusionThe overall performance of our proposed framework may suggest that it could assist medical experts in more accurately identifying and diagnosing patients with hepatitis, dermatology conditions, hepatic disease, and autism.

Comparison of body composition assessment tools in infancy

The prevalence of childhood obesity is increasing globally(1). While BMI is commonly used to define obesity, it is unable to differentiate between fat and muscle mass, leading to calls to measure body composition specifically(2). While several tools are available to assess body composition in infancy, it is unclear if they are directly comparable. Among a subset of healthy infants born to mothers participating in a randomised controlled trial of a preconception and antenatal nutritional supplement(3), measurements were made at ages 6 weeks (n = 58) and 6 months (n = 70) using air displacement plethysmography (ADP), whole-body dual-energy X-ray absorptiometry (DXA), and bioelectrical impedance spectroscopy (BIS). Estimates of percentage fat mass (%FM) were compared using Cohen’s kappa statistic (κ) and Bland-Altman analysis (4,5). There was none to weak agreement when comparing tertiles of %FM (κ = 0.15–0.59). When comparing absolute values, the bias (i.e., mean difference) was smallest when comparing BIS to ADP at 6 weeks (+1.7%). A similar bias was observed at 6 months when comparing DXA to ADP (+1.8%). However, when comparing BIA to DXA at both ages, biases were much larger (+7.6% and +4.7% at 6 weeks and 6 months, respectively). Furthermore, there was wide interindividual variance (limits of agreement [LOA] i.e., ± 1.96 SD) for each comparison. At 6 weeks, LOA ranged from ± 4.8 to ± 6.5% for BIA vs. DXA and BIA vs. ADP, respectively. At 6 months, LOA were even wider, ranging from ± 7.3 to ± 8.1% (DXA vs. ADP and BIA vs. DXA, respectively). Proportional biases were apparent when comparing BIS to the other tools at both ages, with BIS generally overestimating %FM more among infants with low adiposity. In addition to differences according to tool type, within-tool factors impacted body composition estimation. For ADP measurements, the choice of FFM density reference (Fomon vs. Butte) had minimal impact; however, choice of DXA software version (GE Lunar enCORE basic vs. enhanced) and BIS analysis approach (empirical equation vs. mixture theory prediction) led to very different estimates of body composition. In conclusion, when comparing body composition assessment tools in infancy, there was limited agreement between three commonly used tools. Therefore, researchers and clinicians must be cautious when conducting longitudinal analyses or when comparing findings across studies, as estimates are not comparable across tools.

Measurement of Ξc+ production in pPb collisions at sNN=8.16 TeV at LHCb

A study of prompt Ξc+ production in proton-lead collisions is performed with the LHCb experiment at a center-of-mass energy per nucleon pair of 8.16 TeV in 2016 in pPb and Pbp collisions with an estimated integrated luminosity of approximately 12.5 and 17.4 nb−1, respectively. The Ξc+ production cross section, as well as the Ξc+ to Λc+ production cross-section ratio, are measured as a function of the transverse momentum and rapidity and compared to the latest theory predictions. The forward-backward asymmetry is also measured as a function of the Ξc+ transverse momentum. The results provide strong constraints on theoretical calculation and are a unique input for hadronization studies in different collision systems. ©2024 CERN, for the LHCb Collaboration 2024 CERN

ZnS and CdS counterparts of biphenylene lattice: A density functional theory prediction

This study presents four novel inorganic structures based on the biphenylene network (BPN): planar BPN-ZnS (p-BPN-ZnS) and BPN-CdS (p-BPN-CdS) and buckled BPN-ZnS (b-BPN-ZnS) and BPN-CdS (b-BPN-CdS). Cohesive energy analyses reveal that structural buckling enhances stability, and a perturbation is necessary to obtain planar lattices. Phonon dispersion and ab initio molecular dynamics (AIMD) simulations demonstrated the dynamical and thermal stabilities. ZnS-based structures exhibited more pronounced charge accumulation and depletion than CdS. All evaluated structures are ultra-wideband gap semiconductors, with band gap energy values of 4.33, 5.34, 3.59, and 4.30 eV (at HSE06 level) for p-BPN-ZnS, b-BPN-ZnS, p-BPN-CdS, and b-BPN-CdS, respectively. p-BPN-ZnS demonstrated the highest Young modulus (Yx/Yy = 25.295/34.874 N/m), followed by p-BPN-CdS (Yx/Yy = 15.286/21.339 N/m). On the other hand, b-BPN-ZnS and b-BPN-CdS exhibit lower Young Modulus, Yx/Yy = 4.135/14.709 and 11.842/8.218 N/m, respectively. Notably, b-BPN-ZnS displayed a particular characteristic, a negative Poisson ratio (νx/νy = -0.008/-0.030), being an auxetic material. This report is expected to stimulate both theoretical and experimental researchers in the prediction and development of new inorganic materials based on the biphenylene network.

Revisiting the wetting behavior of solid surfaces by water-like models within a density functional theory

We perform the analysis of predictions of a classical density functional theory for associating fluids with different association strength concerned with wetting of solid surfaces. The four associating sites water-like models with non-associative square-well attraction parametrized by Clark et al. [Mol. Phys., 2006, 104, 3561] are considered. The fluid-solid potential is assumed to have a 10-4-3 functional form. The growth of water film on the substrate upon changing the chemical potential is described. The wetting and prewetting critical temperatures, as well as the prewetting phase diagram are evaluated for different fluid-solid attraction strength from the analysis of the adsorption isotherms. Moreover, the temperature dependence of the contact angle is obtained from the Young equation. It yields estimates for the wetting temperature as well. Theoretical findings are compared with experimental results and in a few cases with data from computer simulations. The theory is successful and quite accurate in describing the wetting temperature and contact angle changes with temperature for different values of fluid-substrate attraction. Moreover, the method provides an easy tool to study other associating fluids on solids of importance for chemical engineering, in comparison with laboratory experiments and computer simulations.

Bi-Solitons on the Surface of a Deep Fluid: An Inverse Scattering Transform Perspective Based on Perturbation Theory.

We investigate theoretically and numerically the dynamics of long-living oscillating coherent structures-bi-solitons-in the exact and approximate models for waves on the free surface of deep water. We generate numerically the bi-solitons of the approximate Dyachenko-Zakharov equation and fully nonlinear equations propagating without significant loss of energy for hundreds of the structure oscillation periods, which is hundreds of thousands of characteristic periods of the surface waves. To elucidate the long-living bi-soliton complex nature we apply an analytical-numerical approach based on the perturbation theory and the inverse scattering transform (IST) for the one-dimensional focusing nonlinear Schrödinger equation model. We observe a periodic energy and momentum exchange between solitons and continuous spectrum radiation resulting in repetitive oscillations of the coherent structure. We find that soliton eigenvalues oscillate on stable trajectories experiencing a slight drift on a scale of hundreds of the structure oscillation periods so that the eigenvalue dynamics is in good agreement with predictions of the IST perturbation theory. Based on the obtained results, we conclude that the IST perturbation theory justifies the existence of the long-living bi-solitons on the surface of deep water that emerge as a result of a balance between their dominant solitonic part and a portion of continuous spectrum radiation.