Triadic Interactions Research Articles

Parental insightfulness is associated with mother-father-child interactions among families of preschoolers with an Autism Spectrum Disorder diagnosis.

Parental insightfulness underlies parental sensitive behavior and is associated with secure attachment among Typically Developing (TD) children and also among children with Autism Spectrum Disorder (ASD). Moving beyond the parent-child dyad, a study of TD children and their parents linked mothers' and fathers' combined insightfulness to triadic interactions. The goal of the current study was to examine this association in families with children with ASD. The hypothesis was that the interactions in families in which both parents are insightful will be more cooperative than in families in which only one or neither parent was insightful. Eighty preschooler boys with ASD and both of their parents participated in the study. Parental insightfulness was assessed employing the Insightfulness Assessment (IA) and mother-father-child interactions were observed and coded employing the Lausanne Triadic Play (LTP) procedure. As expected, families in which both parents were insightful displayed higher parental coordinated support in the LTP than families in which one or neither parent was insightful, controlling for children's IQ and severity of symptoms. Children's engagement with their parents was associated with their IQ and severity of symptoms but not with parental insightfulness. The importance of considering paternal, in addition to maternal insightfulness as a foundation for parental coordinated support in family interactions, is discussed, as well as the contribution of the LTP in assessing family interactions with children diagnosed with ASD.

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

Pure Inertial Waves Radiating From Low‐Frequency Flows Over Large‐Scale Topography

AbstractMooring data collected at a flat‐topped seamount suggest the generation of pure inertial waves (PIWs; waves with a dominant frequency equal to the local inertial frequency f) by low‐frequency flows over large‐scale topography. Energetic PIWs were observed within a narrow depth range (∼100 m) near the seafloor at the edge of the summit. These waves could be associated with low‐frequency flows. A two‐dimensional nonhydrostatic model was used to show that the observed PIWs are most likely internal wave beams generated by low‐frequency flows over the seamount. Two types of PIWs were identified via observation and model. The first is a PIW that can only travel horizontally. The other propagates upward, with super‐inertial intrinsic frequency that is Doppler‐shifted by the flows to f. Nonlinear triadic interactions among waves with the frequencies [0, f, f] may transfer energy from mean flows to PIWs, promoting energy decay of geostrophic flows over large‐scale topography.

Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (Phys. Rev. E, vol. 68, 2003, 015301), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov–Zakharov spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ( $\perp$ ) and parallel ( $\parallel$ ) directions to the rotation axis, we show numerically that in the latter case some triadic interactions can have a negative contribution to the energy flux, while in the former case all interactions contribute to a positive flux. Neglecting the parallel energy flux, we estimate the Kolmogorov constant at $C_K \simeq 0.749$ . These results provide theoretical support for recent numerical and experimental studies.

Global modes of variable-viscosity two-phase swirling flows and their triadic resonance

The linear and nonlinear dynamics of two-phase swirling flows produced by the Grabowski–Berger profile under the influence of a viscosity stratification are investigated. We perform axisymmetric nonlinear simulations and fully three-dimensional linear global stability analysis of the flow for several swirl numbers $S$ and viscosity ratios $\tilde {\mu }$ . They are accompanied by nonlinear three-dimensional simulations and subsequent modal analysis using the bispectral mode decomposition, recently introduced by Schmidt (Nonlinear Dyn., vol. 102, issue 4, 2020, pp. 2479–2501). We find a pronounced destabilising effect of the viscosity stratification on both the onset of axisymmetric vortex breakdown and helical instability that is linked to the required shear stress continuity across the interface. Consequently, destabilisation is shifted to lower $S$ as compared with an equivalent flow with uniform viscosity. Further, the stability analysis reveals the simultaneous destabilisation of two global modes with wavenumbers $m=1$ and $m=2$ that have harmonic frequencies. The analysis of the nonlinear flow reveals a strong triadic resonance between these modes that governs the nonlinear dynamics and leads to a rapid departure from the linear dynamics. At larger swirl, the bifurcation of additional modes initiates an interaction cascade by means of triadic resonance which is elucidated by the bispectral analysis. It leads to the emergence of a variety of additional modes in the nonlinear flow. This study contributes to an improved understanding of the influence of viscosity stratification on the onset of vortex breakdown and the destabilisation of global modes. Further, it provides a clear picture of the dynamics of swirling flows with a codimension-two point and related triadic interaction of two global modes at harmonic frequencies and wavenumbers.

Using the live assessment to discriminate between Autism Spectrum Disorder and Disinhibited Social Engagement Disorder

BackgroundChildren with Autism Spectrum Disorder (ASD) and children with Disinhibited Social Engagement Disorder (DSED) may present with similar social problems, despite differing aetiologies, resulting in diagnostic conundrums. MethodsThirty children: 10 with ASD, no maltreatment history, 10 with DSED and 10 typically developing children were assessed via ‘gold standard’ ASD assessments, including the Autism Diagnostic Observational Schedule (ADOS) and a unique unstructured observation known as the Live assessment. Live utilises a triadic interaction (2 assessors and child), playful teasing and social ‘stress’ scenarios to increase the social challenge. ResultsThe ADOS supported discrimination of DSED from ASD to a degree. Where additional neurodevelopmental problems created ambiguity, the Live assessment was more supportive than the ADOS for unpicking the underlying nature of the social problems. ConclusionLive supported differentiation between ASD, DSED and other neurodevelopmental problems. The greater social challenge presented by Live exacerbated core problems of ASD and, in DSED, core social skills stood out.

Evolution of dissipative fluid flows with imposed helicity conservation

We propose the helicity-conserved Navier–Stokes (HCNS) equation by modifying the non-ideal force term in the Navier–Stokes (NS) equation. The corresponding HCNS flow has strict helicity conservation, and retains major NS dynamics with finite dissipation. Using the helical wave decomposition, we show that the pentadic interaction of Fourier helical modes in the HCNS dynamics is more complex than the triadic interaction in the NS dynamics, and enhanced variations for left- and right-handed helicity components cancel each other in the HCNS flow to keep the invariant helicity. A comparative study of HCNS and NS flow evolutions with direct numerical simulation elucidates the influence of the helicity conservation on flow structures and statistics in the vortex reconnection and isotropic turbulence. First, the HCNS flow evolves towards a Beltrami state with a $-4$ scaling law of the energy spectrum at high wavenumbers at long times. Second, large-scale flow structures are almost identical during the viscous reconnection of vortex tubes in the two flows, whereas many more small-scale helical structures are generated via the pentadic mode interaction in the HCNS flow than in the NS flow. Moreover, we demonstrate that parity breaking at small scales can trigger a notable helicity variation in the NS flow. These findings hint that the helicity may not be conserved in the inviscid limit of the NS flow.

The structure of energy fluxes in wave turbulence

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

Intercultural Mediation and its Conflicting Allegiances in Slovenia

The article examines intercultural mediation which is a relatively new profession aimed at assuring equity in access to various institutions, including those in the field of healthcare. Based on qualitative research with intercultural mediators in Slovenia, the article analyses the power relations that arise in the triadic interactions in healthcare worker–patient–intercultural mediator relationships. We explore the role of intercultural mediators in relation to the two sides that they are supposed to connect: the side of the patients and the side of healthcare workers. Paying attention to power relations, we show how intercultural mediators’ shifting allegiances between patient and healthcare workers considerably shape their practice.

Locomotion development and infants' object interaction in a day-care environment.

This longitudinal study examined the relationship between the development of locomotion and infants' interaction with others involving objects. Observations took place in a multi-person situation-a day-care class-for one-year-old infants for 1year. The study participants were 13 infants and 7 caregivers (all Japanese). Frequencies of infants' manual contact with objects and moving before contact with them did not differ according to locomotion developmental level. However, infants who began walking engaged in more social interactions than those who were cruising or crawling. Throughout all locomotor developmental periods, social interactions increased in frequency when more caregivers were present. As infants began to walk, they moved more prior to social interactions, had more frequent bidirectional and triadic social interactions, and moved and interacted more often with others during a single object episode. These results suggest that crawlers' engagement with objects is relatively object-oriented, while for walkers, locomotion seems to be driven by social stimuli. Infants who have begun to walk moved among caregivers and peers in a multi-person environment and developed more elaborated social interactions through objects.

The long view of triadic resonance instability in finite-width internal gravity wave beams

This article presents our exploration into how a finite-width internal gravity wave beam is modified by triadic resonance instability. We present both experimental and weakly nonlinear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability evolves over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly nonlinear theory, we find that the wave does not monotonically approach a saturated equilibrium of triadic interactions; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour, we develop a weakly nonlinear approach to account for the spatiotemporal evolution of the amplitudes and structures of the beams over slow time scales and long distances, and explore the consequences using a numerical scheme to solve the resulting equations. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatiotemporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

Structural filtering of functional data offered discriminative features for autism spectrum disorder.

This study attempted to answer the question, "Can filtering the functional data through the frequency bands of the structural graph provide data with valuable features which are not valuable in unfiltered data"?. The valuable features discriminate between autism spectrum disorder (ASD) and typically control (TC) groups. The resting-state fMRI data was passed through the structural graph's low, middle, and high-frequency band (LFB, MFB, and HFB) filters to answer the posed question. The structural graph was computed using the diffusion tensor imaging data. Then, the global metrics of functional graphs and metrics of functional triadic interactions were computed for filtered and unfiltered rfMRI data. Compared to TCs, ASDs had significantly higher clustering coefficients in the MFB, higher efficiencies and strengths in the MFB and HFB, and lower small-world propensity in the HFB. These results show over-connectivity, more global integration, and decreased local specialization in ASDs compared to TCs. Triadic analysis showed that the numbers of unbalanced triads were significantly lower for ASDs in the MFB. This finding may indicate the reason for restricted and repetitive behavior in ASDs. Also, in the MFB and HFB, the numbers of balanced triads and the energies of triadic interactions were significantly higher and lower for ASDs, respectively. These findings may reflect the disruption of the optimum balance between functional integration and specialization. There was no significant difference between ASDs and TCs when using the unfiltered data. All of these results demonstrated that significant differences between ASDs and TCs existed in the MFB and HFB of the structural graph when analyzing the global metrics of the functional graph and triadic interaction metrics. Also, these results demonstrated that frequency bands of the structural graph could offer significant findings which were not found in the unfiltered data. In conclusion, the results demonstrated the promising perspective of using structural graph frequency bands for attaining discriminative features and new knowledge, especially in the case of ASD.

Assessing Triadic Interactions and the Family Alliance among Belgian Lesbian Mothers and Their Donor-Conceived Children

Both empirical and clinical evidence with heterosexual parents and their biological children has shown the significant influence of early family interactions on children’s socioemotional and cognitive development during their first years. Yet, very little research has applied family-level assessment to families who are diverse with respect to parents’ gender and sexual orientation, and child’s method of conception. The present cross-sectional study compared 24 lesbian mother families with donor-conceived children and 24 heterosexual parent families with spontaneously conceived children with respect to triadic interaction quality and the family alliance (i.e., emotional and interactional coordination during family activities), as observed during the Lausanne Trilogue Play procedure. All parents were first-time parents, White, cisgender, residing in Belgium, had an upper-middle socioeconomic status, and a child aged 3–74 months (M = 21.00, SD = 17.72). Across family types, triadic interactions demonstrated similar scores in each family alliance dimension, characterized by appropriate levels of participation, organization, focalization, and affect sharing. The results have clinical implications for the use of the LTP as both a clinical assessment and a tool to reinforce and intervene with lesbian coparents. Family psychologists may find the results particularly informative when working to support coparenting relationships among diverse families.

Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes

Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades over simplicial complexes that encode dyadic, triadic and higher-order interactions. Focusing on small-world models containing both short- and long-range k-simplices, we explore spatio-temporal patterns that manifest as a frustration between local and nonlocal propagations. We show that higher-order interactions and nonlinear thresholding coordinate to robustly guide cascades along a k-dimensional generalization of paths that we call ‘geometrical channels’. We also find this coordination to enhance the diversity and efficiency of cascades over a simplicial-complex model for a neuronal network, or ‘neuronal complex’. We support these findings with bifurcation theory and data-driven approaches based on latent geometry. Our findings provide fruitful directions for uncovering the multiscale, multidimensional mechanisms that orchestrate the spatio-temporal patterns of nonlinear cascades.

The Role of Family Function and Triadic Interaction on Preterm Child Development-A Systematic Review.

Preterm infants are at high risk of developmental disability/delay and are more dependent on their caregiving environment for regulation due to their neurological immaturity. A premature birth is also a major stressor to the family system that constitutes the infant's caregiving environment. The following systematic review investigates whether families with preterm children differ from families with full-term children in their interactions, and what impact the quality of family interaction has on child development. Using the Cochrane model, we conducted a systematic review of quantitative studies published in psycINFO, socINDEX, and PubMed, concerning family quality in triadic interactions in families with premature infants and children, and at least one child development outcome variable. The quality of these studies was assessed using the Newcastle-Ottawa scale assessment form for cohort studies (NOS). Eleven studies were included in the review. Quality of family interactions is either equal to or poorer in families with preterm children, compared with families with full-term children. Importantly, the link between quality of family interactions and child development outcome is stronger in preterm children compared with full-term children, regarding both positive and negative influence. Our results highlight the importance of strengthening family interactions in order to promote development in preterm children. Notably, this review provides the first systematic overview of family function and the quality of triadic interactions in preterm families. The limited number of studies with a family-system focus makes it difficult for us to draw any definitive conclusions, while underscoring the need for more observational studies, particularly post-infancy, to be able to identify specific aspects of family interactions that may be critical for preterm child development.

Intervention, war expansion, and the international sources of civil war

Why do some civil wars turn into interstate wars? I analyze an asymmetric information model of civil war onset, rebel-sided intervention, and interstate retaliation with endogenous stakes. Interstate war occurs when rebels believe that the threat of intervention will compel the government to acquiesce, the third party believes that the government will tolerate an intervention, but they both underestimate the government's resolve. The model also has implications for civil wars. Retaliation can deter intervention and rebellion, but intervention can compel the government to give up power, so predicting civil war requires accounting for this triadic interaction.

Resonant growth of inertial oscillations from lee waves in the deep ocean

The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.

Examining supplier, buyer, and customer triads: The critical role of conflict in interaction processes and product/service innovations

As solutions in business-to-business markets become more complex, firms embed external products and services to better cater to customer needs. Complex solutions sometimes lead to triadic relationships, where interactions emerge between the supplier, the business-to-business buyer, and their customers. Infrequent examination of these relationships led this research to focus on understanding the interaction and innovation processes in triadic relationships. Using a single longitudinal case study, this study discovered four key outcomes that emerged from triadic interactions—product enhancement, service refinements, e-resource integration, and complementary synergy. These outcomes corresponded with a movement from a linear relationship (supplier with buyer and buyer with the customer) to a network relationship (each member has a relationship with other members). Surprisingly, our findings indicated that conflict is an antecedent to cooperation and the development of triadic relationships. Finally, shallow triadic relationships lead to incremental innovation, but deep triadic relationships lead to radical innovation. From our findings, we derive implications for theory and practice.

Alpha and theta brain activity in 9-month-old infants during a live referential gaze paradigm.

The ability to establish a connection between the direction of the other's gaze and the object that is observed has important implications in the development of social cognition and learning. In this study, we analyzed alpha and theta band oscillations in one group of 9-month-old infants by implementing a face-to-face live paradigm, which presented the infants with a triadic social interaction with a real human being. We compared neural activations in two experimental conditions: Congruent and Incongruent gaze shift following the appearance of an object. In the Incongruent object-gaze shift condition, we observed an increase of the theta power in comparison with the Congruent condition. We also found an enhancement of the alpha activity during the Congruent versus the Incongruent object-gaze condition. These findings confirm the involvement of the theta and alpha band activity in the detection of the gaze of others when it shifts toward a referential target. We consider that the theta band modulation could be associated with the processing of unexpected events. Furthermore, the increase of the alpha band activity during the Congruent object-gaze condition seems to be in agreement with prior findings on the mechanisms of internally controlled attention that emerge before the first year of life. The implementation of a live paradigm elicited a partially different oscillatory pattern in comparison with non-live standard paradigms, supporting the importance of an ecological set-up reproducing real-life conditions to study the development of social cognition.

Mothers’ and fathers’ bimodal communication in dyadic and triadic interaction with their infants

Parents play an important role in children’s language development. To our knowledge, no studies have compared fathers’ and mothers’ use of gestural and verbal communication in dyadic versus triadic contexts. This study aimed at analyzing similarities and differences in the bimodal communication of parents when they play alone with their infant and when all three play together. Twelve Italian-speaking families with infants aged 16 months took part in the study. Dyadic and triadic free-play interactions of mothers and fathers with their infants were videotaped. Mothers’ and fathers’ communicative acts (i.e., ‘only speech’, ‘only gesture’, ‘speech + gesture’), and types of gestures (i.e., deictic, representational, and emphatic) were coded. Results showed that infants experience mothers’ and fathers’ bimodal communication when interacting with both parents. In the dyadic context, mothers produced more communicative acts and more verbal communication than fathers who in turn used more gestures and ‘speech + gesture’ communicative acts than mothers. Both parents used gestures to clarify and reinforce their verbal communication in dyadic and triadic contexts. With respect to the triadic context, no differences between mothers’ and fathers’ verbal and non-verbal communication emerged. Comparing each parent across the two contexts, findings showed that in the triadic context, mothers increased their use of gestural communicative acts and decreased their use of mixed acts, whereas fathers increased their verbal component while decreasing their ‘speech + gesture’ communicative acts. It seems that in the triadic context there is a coordination between parents that leads them to align with the kind of communication provided to the infant. Thus, the input experienced by infants in the triadic context is still equally composed of both verbal and non-verbal communication. Results are discussed considering the role of parents’ bimodal communication within several daily interactional contexts.