Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of ‘open’ reaction–diffusion systems often neglect the role of domain boundaries. Most idealizations of closed reaction–diffusion systems employ no-flux boundary conditions, and often patterns will form up to, or along, these boundaries. Motivated by boundaries of patterning fields related to the emergence of spatial form in embryonic development, we propose a set of mixed boundary conditions for a two-species reaction–diffusion system which forms inhomogeneous solutions away from the boundary of the domain for a variety of different reaction kinetics, with a prescribed uniform state near the boundary. We show that these boundary conditions can be derived from a larger heterogeneous field, indicating that these conditions can arise naturally if cell signalling or other properties of the medium vary in space. We explain the basic mechanisms behind this pattern localization and demonstrate that it can capture a large range of localized patterning in one, two, and three dimensions and that this framework can be applied to systems involving more than two species. Furthermore, the boundary conditions proposed lead to more symmetrical patterns on the interior of the domain and plausibly capture more realistic boundaries in developmental systems. Finally, we show that these isolated patterns are more robust to fluctuations in initial conditions and that they allow intriguing possibilities of pattern selection via geometry, distinct from known selection mechanisms. Reaction–diffusion systems (RDS) are employed to model an increasingly wide-range of phenomena Ball . FollowiStationary Turing patterns, as well as other complex behaviours of RDS such as oscillations and chemical chaos, are genuinely non-equilibrium thermodynamic processes. Since the early work of Nicolis and Prigogine . Examples include ectodermal structures such as hair or teeth  or due to more complex and diffuse mechanisms involving cell state, which may be refined into sharp boundaries via, e.g. bistability. Such boundaries can be thought of as an example of positional information  in biological systems. These undergo processes of synthesis, decay, and diffusion, depending on the type of molecule employed as a signal. Most intercellular communication is achieved through gene-encoded polypeptides (proteins), with some smaller molecules also playing roles as diffusible signals. The synthesis of these signals is largely controlled by rates of gene expression (transcription and translation) within cells, directly in the case of proteins, and for small molecules indirectly through production of enzymes that catalyse their formation. These molecules are secreted from cells, then diffuse, either alone or interacting with other proteins, through subcellular structures, or the meshwork of extracellular matrix. Ultimately, these molecules are capable of attaching to receptors on the surface of, or sometimes within, cells in the vicinity. The effect of receptor binding is to trigger a typically multi-step process of signal transduction, ultimately altering rates of gene expression (molecule synthesis), or cell behaviour (such as cell shape or movement)  family, several members of which have been implicated in reaction–diffusion periodic patterning systems of skin  that the specificity of molecular interactions is very high and (ii) that the candidate activator and inhibitor molecules in many systems do not interact directly, but rather through chains of intermediates in signalling pathways. The specificity of molecular interactions and indirect nature of activator–inhibitor interaction permit selective spatial variation in the properties of the activator and inhibitor that we will explore in this paper. Boundaries relevant to reaction–diffusion patterning will be defined by the geometry of the embryo or organ, and by spatial variation in the expression of genes that encode or modulate activator and inhibitor synthesis, diffusion, biological activity, and decay. Geometric boundaries are unavoidable and often prominent in experimental systems at the cut edges of the tissue, as they have a strong influence on pattern formation  can arise from previous patterning events, such as an external organizing region emitting a graded signal that influences part of the patterning field. Graded boundaries may persist in that form, or can be refined into sharp boundaries by, for example, the action of mutually antagonistic factors that create bistable systems, notable in the formation of discrete segments  in the reaction–diffusion system, which will be free to diffuse across the boundary and persist physically, but without the ability to influence reaction kinetics in this region of the field.v is a self-inhibitor, u and v as presumptive activator and inhibitor, respectively.We now consider modelling such boundaries in a reaction–diffusion system. Throughout the paper, we will consider a generic two-species RDS in the domain R should be approximately a minimum of u in a patterned state (e.g. with Neumann boundary conditions). Specifically, if we compute a stable steady-state solution given Neumann boundary conditions and initial data perturbed from the homogeneous equilibrium, we will take R seems to play only a small role in influencing the pattern, at least for some reaction kinetics. While it can have quantitative effects on the size and spacing of localized solutions, our numerical results suggest that taking R less than the homogeneous steady state suffices to lead to interior patterning. In some sense this is obvious, as we are fixing the value of u at the boundary. We will focus on the case where the activator is fixed at the boundary and the inhibitor is not allowed to diffuse (i.e. satisfies zero flux conditions). In principle, our results on interior localization will hold if we swap the boundary conditions between activator and inhibitor, but the lengthscale of the boundary influence will be larger in the case of the inhibitor being fixed  can be isolated away from the domain boundary. This can be achieved by using the boundary conditionsu and v as behaving differently outside the domain u represents temperature, and v a chemical which undergoes exothermic or endothermic reactions  in the medium. Within the interior region, One can show that for sufficiently large  of Eqs. –5) can, can,\docmentclass2pt{minimnditions . In highu and v outside the interior domain are simple and  determined analytically. In particular, with v on v; in one spatial dimension the restriction of We proceed to show that for sufficiently large mentclass2pt{minimn system  defined  problem –5) need need\docmentclass2pt{minimtates of  will be tates of –(5). SimOur first objective is to determine how the solution within the interior of the boundary of u will have an identical expansion.The mollified steady-state equations on the extended domain arend Sneyd ]. Using v is linear in u in this region. However, boundedness of this inner solution when leaving the transition region ,12\d,12\d2),1+ in Eq. . In partv, that is In summary, we have that, providing  of Eqs. –5) on \ on \\docmentclasspt{minimau and v, but only a subset of these satisfy the mixed conditions  using periodic, Neumann, and mixed boundary conditions. We employ a method-of-lines approach to simulate the RDS, using the standard three-point stencil to discretize the Laplacian. We use the MATLAB function ‘ode15s’ to evolve these ordinary differential equations in time, and the MATLAB function ‘fsolve’ to compute steady-state solutions to the discretized system on i. Starting with periodic boundary conditions, we evolve this initial condition for To demonstrate this concretely, we simulate the Schnakenberg kinetics from Table R equal to the minimal value of u from the Neumann case in (c), and conditions . Finally, using We use these ten shifted periodic solutions as initial conditions for simulating the RDS using three other sets of boundary conditions and then again find stable steady states after evolution in time. We use Neumann conditions in Fig. nditions  with \doR as the minimal value of u from these simulations with Neumann conditions ), we obtain a single solution with mixed conditions in (c). Setting R equal to either the other minimum of u from the Neumann conditions, or to 0, has only a small influence on the solution near the boundary, as can be seen in (d). The mixed boundary conditions further exclude half-integer mode solutions.More generally, solutions satisfying Neumann boundary conditions need not give rise to periodic patterns, particularly if the domain permits half-integer modes Murray . In Fig.v is extremal and u is minimal at the same points which satisfy both Neumann and periodic boundary conditions will also satisfy the conditions . It is not always the case that reaction–diffusion patterns will have both species sharing extremal points, but this can be shown near a Turing bifurcation via linearization, and is observed (at least approximately) in many systems numerically beyond the bifurcation , in addition to stripe orientation.Throughout these examples, we will use the Schnakenberg kinetics from Table First we consider circular and elliptical domains in Fig. u as a stripe, then the confined patterns generated by mixed boundary conditions all have exactly four of these. This is despite the fact that the largest ellipse occupies three times the area of the circle, and these observations appear to be robust to different random perturbations of the initial conditions. Finally, these results are relatively insensitive to the value of R, as simulations with u in the Neumann cases was In each of the cases with Neumann boundary conditions, there are slightly different numbers of stripes (depending on what one classifies as a stripe), with (c) having the largest number for these simulations. Different random initial conditions can lead to substantial variation in the number of such structures, depending on what orientation most stripes take. In contrast, if one considers a contiguous region of higher-than-average values of L is now a measure of the domain length , gav, gav\doce system  (not shoWe have chosen the species with a fixed Dirichlet boundary condition here to be  part of ). We shon species will have qualitatively similar effects. Without loss of generality, the arguments given in Sect. n species case as long as all constraints are satisfied. In particular, we anticipate that placing the Dirichlet condition on any single species will confine the patterns to the interior via the same mechanism suggested in Sect. R different from what is stated in Sect. While this is only a single example of a multispecies model, we anticipate that the generalization to Isolation of patterns in reaction–diffusion systems (RDS) on the interior of a domain can be motivated both phenomenologically, by observing patterning fields which are clearly subsets of a given region, or mechanistically in terms of boundaries in gene expression. Such gene expression boundaries themselves can either emerge due to previous cell fate specification or local signalling dynamics. Here we have developed a novel method of inducing such isolated patterns with a simple change in the boundary conditions governing the RDS. We have justified these boundary conditions by considering heterogeneous RDS modelling a change in reaction dynamics explicitly and shown that such systems can reduce asymptotically to RDS satisfying these mixed boundary conditions at steady state, given weak geometric and kinetic constraints. This is consistent with the theoretical literature showing pattern localization and modulation in heterogeneous environments (Varea et al. As described in the introduction, there are still major gaps in our understanding of RDS, particularly as models in developmental biology. While the original formulation of Turing’s theory is a powerful and simple way of obtaining periodically patterned states, it suffers from a number of robustness problems, in part due to this simplicity (Maini et al. While we focused on analyzing terminal steady-state patterns, we remark that the boundary conditions  often haentclass1pt{minimaFinally, we mention that our results also demonstrate a novel application of domain geometry in robustly giving rise to patterns of qualitatively different types. Specifically, in Fig. Many periodic patterns in development are spatially localized within some region of an otherwise homogeneous tissue. There are at least three distinct ways that such regionalization can occur, as described in Sect. R in more general systems, as discussed in Sect. As mentioned in the introduction, Neumann boundary conditions can also exhibit isolated patterning if the initial data consist of internal spot solutions (Kolokolnikov et al. D, the shadow-limit approaches of Ward et al. (There are numerous other extensions of the basic ideas here, but we restrict attention to five possible areas of future work. As above, there is work to be done in more rigorously justifying our conclusions regarding equilibria, pattern selection, and transient dynamics. As the examples in Table d et al.  (and mand et al.  and elsed et al. . Finallyd et al. . Prelimid et al. ]. While


Languages vary with respect to whether sentences with two negative elements give rise to double negation or negative concord meanings. We explore an influential hypothesis about what governs this variation: namely, that whether a language exhibits double negation or negative concord is partly determined by the phonological and syntactic nature of its negative marker (Zeijlstra  Jan rent niet.Jan run NEG.‘Jan doesn’t run’Niemand rent.N-body run.‘Nobody runs’Niemand rent niet.N-body run NEG.‘Nobody doesn’t run’ In many other languages, however, the combination of two or more negative expressions can yield a single semantic negation, constituting what is usually known as negative concord. Consider the following example from Serbian: (3)Niko ne trčiN-body NEG run‘Nobody run’Despite containing both a negative particle (‘ne’) and a negative existential (‘niko’), the sentence in (3) does not lead to a double negation reading as in (2), but to a single negation interpretation. Languages like Serbian are thus known as negative concord languages. While the class of languages that allow negative concord interpretations is far from homogeneousstrictly negative concord (Giannakidou n-words or negative concord items (NCIs) (Laka (4)*Niko trči.*N-body run.Ko trči? Niko.who came? N-body‘Who came?’ Nobody.The contrast between (2) and (3) illustrates the existence of cross-linguistic variation with respect to the interpretation of sentences with multiple negative expressions. A natural question, then, is what determines the distribution of double negation and negative concord interpretations. Debates in the literature have mostly centered on whether negative concord or double negation should be considered the default interpretation for these multiple-negation sentences, and on whether their interpretation might be explained by other linguistic properties  necessarily contributes an independent semantic negation. For example, as illustrated in 1-a) and (1-b), in Dutch, both the negative marker ‘niet’ and the negative indefinite ‘niemand’ can independently be used to express sentential negation. But when these negative elements are -a and  Laka  to diffeDe Swart .Evidence from typology and acquisition has been used to support the hypothesis that, despite featuring an apparent violation of compositionality, negative concord is actually more primitive than double negation. For instance, languages that exhibit negative concord seem to be more frequent typologically than those that exhibit double negation  and (3) can receive. In particular, this cross-linguistic variability has been attributed to differing properties of negative indefinites or of negative markers  reflects a cognitive constraint on possible languages. We do this by testing whether learners are sensitive to the correlation between the status of the negative marker and the interpretation of a sentence with two negative elements. We expose English-speaking adult learners to one of four miniature artificial languages which vary along these two dimensions: affixal vs. adverbial negative marker and double negation vs. negative concord interpretation. We predict that, if the Jespersen-Zeijlstra generalization reflects a cognitive constraint (or bias), then languages which are ruled out by the generalization should be harder to acquire than those which are not. That is: learners are expected to find it more difficult to learn a double negation language when the negative marker is an affix than when it is an adverb. By contrast, learners are not predicted to differ in their ability to learn negative concord based on the status of the negative marker. Crucially, then, we predict an interaction between marker type and interpretation such that the type of negative marker should have a stronger effect when learning a double negation than a negative concord language, regardless of whether participants have an overall preference for one type of interpretation or negative marker.In the experiment we report below, we use English-speaking participants. It is thus worth considering, before we continue, what the impact of using an English-speaking population might be. Traditionally, Standard English has been described as a double negation language and distinguished from specific vernacular varieties of English which are known to instantiate negative concord , 2 proper names, 4 quantifiers and one negative marker. All words were created following English phonotactics and were presented orthographically. The three nonce verbs were “jeck”, “rald” and “fudd”, which referred to the events of ‘running’, ‘rotting’ and ‘eating’ respectively. The nouns were “blan” and “affle”, referring to ‘banana’ and ‘apple’. We additionally used the proper names “John” and “Mary”. There were two universal quantifiers  and two negative existential quantifiers (“midho” and “metha’), which varied in animacy: “idho” and “midho” quantify over human individuals and “etha” and “metha” range over inanimate entities. Quantifiers were similar to each other, following what is found in many natural languages, to facilitate learning.The negative markers in the artificial language differed depending on the Marker condition: the negative marker was either the affix or an adverb. There are a number of dimensions one could in principle choose from in order to differentiate an affix from an adverb, including phonological weight, boundedness, the possibility of movement, etc. Here we chose to focus on morpho-phonological features. The short affix “im” was orthographically attached to the verb, whereas the longer adverb “imek”, was represented by an independent orthographic word. We kept the position of the two elements constant, which has the advantage of minimizing linear order differences between the groups, which are in principle not at stake here.simple and quantificational. In both types, word order was Subject-Verb-Object, and negation appeared immediately after the verb. Table Participants were trained on two types of sentences: neg in Table Simple sentences involved nominal subjects. Each verb form had two possible nominal subjects: the two proper names were used with the verbs corresponding to eating and running events, and the two fruit-denoting nouns with the rotting event. The object in transitive sentences  was randomly selected from the fruit-denoting nouns. Simple sentences could be affirmative or negative  or a negative (NC) meaning.Sentences of the type Neg-Existential–Verb–Participants were additionally trained on quantifiers in isolation, which were used as one-word, fragment answers to English wh-interrogatives. The interrogative could be ‘Who is running?’, ‘What is rotting?’ or ‘Who is eating a banana/apple?’. The quantifiers then serve to describe a situation where either no character/fruit was running/rotting/eating or all of them were.The intended meaning of each sentence in the language was conveyed through a picture, as specified in Table exposure, a comprehension and a production task. The experiment proceeded as follows:The experiment was implemented using JavaScript and presented to participants in a web browser, with all instructions in English. Participants were told they were going to learn a foreign language called Čelniŝki. There were four experimental phases, and each phase included an Phase 1: Training and testing on simple affirmative sentences. Participants were first trained on simple affirmative sentences. In each exposure trial, a simple affirmative sentence appeared in the screen with a corresponding picture . Participants were then tested on their ability to comprehend and produce simple affirmative sentences . On each comprehension trial, participants were instructed to match a sentence in the language with one of two pictures: a target picture, which made the sentence true, and a foil picture, which falsified the sentence. Feedback was provided, indicating whether the response was correct or incorrect and highlighting the correct picture choice. In production trials, participants saw an image, and had to type in a description using the new language. The subject of the sentence was already filled-in in the description field; participants had to complete it. Feedback was provided in the form of the expected answer regardless of the participant’s response.Phase 2: Training and testing on simple affirmative and negative sentences. The basic procedure in this phase was analogous to Phase 1, except that participants were additionally exposed to simple negative sentences. To facilitate the learning of the negative marker, simple affirmative and negative sentences were presented in pairs during the exposure block . The comprehension block included 12 sentence-picture matching trials featuring negative sentences (2 per subject-verb pair) and 6 featuring affirmative sentences (1 per subject-verb pair). Production trials were also presented in pairs of affirmative and negative sentences. On each trial, two contrasting pictures were displayed; e.g., one where a character is running and one where a character is not running. Participants were given the description for one of the pictures and had to type in a description for the other one. As in Phase 1, the subject of the sentence was already provided, and participants had to complete the description. Participants received feedback for their answers.Immediately following completion of Phase 2, participants were asked to translate the 5 content words they had learned so far  and were given feedback on their answers.Phase 3: Training and testing on quantifiers in isolation. During exposure , participants were presented a wh-question in English  and a picture corresponding to the answer. In each picture either all or none of the five characters or fruits were running/rotting/eating. After one second, the answer to the question in the novel language was displayed on the screen. The answer always involved a quantifier. Participants were then tested on their ability to comprehend and produce these quantifiers as answers to wh-questions . These tasks proceeded as in Phases 1 and 2.Phase 4: Training and testing on quantificational sentences. Participants were exposed and then tested on both simple and quantificational sentences. The procedure was similar to Phase 1, but there was no feedback during the comprehension and production tasks. There were 30 exposure trials: 6 for each configuration of simple sentences and quantificational sentences . The comprehension and production blocks included 48 trials each. There were 24 simple and 24 quantificational sentences per block, including 9 in the critical configuration: Neg-Existential–Verb–neg.neg  whose accuracy was below 75% in any production or comprehension task across phases 2 and 3 were excluded. The data of the remaining 124 participants was analyzed . Participants were paid 5 USD for their participation which lasted approximately 25 minutes.Recall that, based on Jespersen-Zeijstra’s generalization, we predict that English-speaking learners will find it easier to learn a double negation language when the negative marker is an adverb than when it is an affix; according to this generalization, languages with affixal negation are necessarily negative concord. For learners in the negative concord condition, we did not predict an effect of marker type; negative concord is possible with either type of negative marker. This should lead to an interaction between Marker and Interpretation in how well participants were able to use sentences with two negative expressions.neg sentence configuration (Phase 4).Following our pre-registration, we analyzed accuracy rates in the comprehension and production of the Neg-Existential–Verb–Responses in comprehension trials  were coded as 1 if the picture selected corresponded to the target image, and as 0 otherwise. Per our pre-registration, comprehension trials whose response times were below 500 milliseconds or above 15000 milliseconds were excluded from the analysis. This led to the exclusion of approximately 3% of the critical trials.neg. Model comparison revealed that, contrary to our predictions, the interaction between Marker and Interpretation was not statistically significant . Crucially, the picture that participants had to describe depended on the Interpretation condition, as indicated in Table Responses in these production trials were coded as 1 if the negative marker was present in the description, and 0 if it was absent. Per our pre-registration, we excluded from the analyses responses where: (a) the average Levenshtein distance between the expected and the actual response was greater than 2; or (b) the negative marker was produced in the wrong position. This led to the exclusion of approximately 7% of the critical trials.neg sentences in critical trials. The results of the model comparison revealed that the interaction between Marker and Interpretation was not significant  and in response times, which can be taken to be a more direct reflection of processing. There are a number of explanations which could account for this asymmetry between double negation and negative concord interpretations. First we will entertain explanations that derive from participants’ native language experience.As mentioned above, English speakers vary with respect to how they interpret sentences with multiple negative elements, and it has been argued that Standard English should be treated as an underlyingly negative concord language . Unfortunately, given that our pre-registered hypothesis does not predict an effect of interpretation, we did not gather this information. That said, there is certainly an argument to be made against this explanation. Standard English speakers have been consistently shown to prefer double negation interpretations of sentences featuring the configuration used in our study, which consists of a negative indefinite in subject position preceding the negative marker . For example, a sentence like “Nobody is not running” in its double negation reading might be felicitous as a response to a statement like “Is everyone running? I thought I saw some people just standing around”, but it is less felicitous out of the blue. One result of this is that double negation sentences tend to be quite rare in languages that allow them (while negative concord sentences would be relatively common in a negative concord language). In our experiment, we prioritized similarity across conditions, such that they differed only on our manipulated variables, Marker and Interpretation. We did not manipulate frequencies of double negation or negative concord interpretations across condition, and we did not provide participants with a specialised context for double negation. However, these choices may have contributed to the asymmetry between conditions we found.10As in comprehension, the apparent dispreference for double negative in production might also be explained by native language transfer, or to the lack of context facilitating double negation. However, it is also possible that an aspect of the production task design may have contributed to this effect as well. Recall that, in critical production trials, participants were provided with a negative indefinite and had to complete the sentence. Our results indicated that participants were more likely to produce the negative marker when the overall meaning was negative than when the resulting meaning was positive. The sentence completion aspect of the design may have led participants to ignore the negative indefinite provided, simply producing a negative marker whenever the sentence is negative, e.g., whenever they have to describe a situation where there is no running happening, and to ignore it otherwise.In addition to the possible explanations outlined above, there are also more general explanations, which may be at play in both comprehension and production. One possibility is that, as has been proposed in the acquisition literature, negative concord is treated as a default by learners  the contracted form ‘n’t’ is more frequent in English adult speech than the longer adverb ‘not’. While there is no evidence that ‘n’t’ is easier to learn than ‘not’ for English-speaking children, nevertheless English-speaking participants might bring an expectation of post-verbal affixal negation to the task. This might in turn result in affixal negation being easier to learn. The relative difficulty of learning a double negation language with affixal negation  might then be masked by an overall preference for post-verbal affixal negation. Notably however, we have no clear independent evidence for this explanation. For example, we do not see any preference for affixal negation in the negative concord conditions.A more compelling possibility is that our experiment is not detecting the hypothesized correlation because the artificial languages are not encoding the pertinent distinction between negative markers. Recall that in this study, we manipulated the orthographic properties of two post-verbal negative markers: a longer independent word (‘imek’) and a shorter affix (‘-im’), which appeared attached to the verbal stem. One might question whether these orthographic differences between markers provide a strong enough cue for learners to treat them as morpho-phonologically distinct. Perhaps if the difference in phonological weight was even bigger, or if the experiment were presented auditorily, these differences would trigger the predicted effect.11More importantly, as discussed above, morpho-phonological features are not necessarily sufficient to trigger the syntactic difference on which Zeijlstra’s theory is based. According to this theory, whether a language is double negation depends on whether it has a negative marker that is a syntactic head. Arguably, if learners in our experiment had more evidence to categorize the marker syntactically , an interaction between marker and interpretation would have emerged.Lastly, it is of course possible that the Jespersen-Zeijlstra generalization does not reflect a cognitive constraint or bias, and should instead be seen as an accidental regularity, perhaps the product of relying on a rather small typological sample. It has been argued, for example, that cross-linguistic variation in the interpretation of sentences with multiple negative elements is actually modulated by the properties of the negative concord items or of negative indefinites, rather than by the properties of the negative marker Déprez .In this paper, we investigated a well-known typological generalization on the distribution and interpretation of negative words: whether a language exhibits double negation or negative concord correlates with the phonological and syntactic nature of its negative marker (Zeijlstra


The plastic industry is undergoing drastic changes, due to the customer sustainability perception of plastics, and the eruption of new processes (such 3D printing) and materials (such as renewably sourced resins). To enable a fast transition to high-quality, sustainable plastic applications, a specific methodology could be a key competitive advantage. This novel methodology is focused on improving the objectivity and efficiency of plastic production and the design review process. It is applicable to discrete optimization events in any product lifecycle milestone, from concept design to serial production stages. The methodology includes a natural way to capture plastic-related knowledge and trends, oriented towards building a dynamic “interaction matrix”, with a list of potential optimizations and their positive or negative impacts in a comprehensive set of multi-criteria evaluations. With an innovative approach, the matrix allows the possibility to incorporate a business strategy, which could be different at every lifecycle stage. The business strategy is translated from the common “verbal” definition into a quantitative set of “Target and Restrictions”, making it possible to detect and prioritize the best potential design optimization changes according to the strategy. This methodology helps to model and compare design alternatives, verify impacts in every evaluation criteria, and make robust and objective information-based decisions. The application of the methodology in real cases of plastic material design optimization in the automotive industry has provided remarkable results, accelerating the detection of improvement methods aligned with the strategy and maximizing the improvement in product competitiveness and sustainability. In comparison with the simultaneous application of existing mono-criteria optimization methodologies (such as “Design to Cost” or “Eco Design”) and subjective expert-based reviews, the novel methodology has a reduced workload and risks, confirming its potential for future application and further development in other polymer-based products, such as consumer goods or packaging. Plastic materials have been a revolution for many markets in previous decades, replacing other materials due to their cost competitiveness, design flexibility, light-weight or decoration and finishing properties, widening the access to convenient products and playing an important role in the development of humanity . In the Companies currently producing or designing plastic products must adapt as fast as possible to market requirements and opportunities, reviewing their product and process design to continuously improve and to detect optimization opportunities to improve competitiveness and sustainability. The development and utilization of specific methodologies for this transition could accelerate this adaptation and represent a key competitive advantage for success and sustainability.Due to the intrinsic subjectivity of product design activities, some studies have attempted to understand and evaluate their designs according to attributes , and impRegarding methods for design review and optimization, in some competitive industries, continuous improvement methods are widely applied, such as Lean, Kaizen or Six-Sigma ,30, alsoAs an example, even if applying some existing plastic design methods ,14,29,30The methodology has the objective of plastic product and process design review and optimization at any product lifecycle milestone, from concept to end of life, in order to make it possible to apply in any company and lifecycle stage.It must be capable of capturing the business strategy, which could be different at each milestone, and must be translated into a set of improvement “target” and restrictions.It is focused on the “multi-criteria” evaluation of design alternatives, the detection of optimization strategies according to targets and restrictions, determining changing impacts and making objective and information-based design decisions.The methodology must be easily integrated as an additional “layer” that is compatible with any company size, organization, design strategy or knowledge management system, without required changes, simplifying its implementation and accelerating knowledge capture and application results.The methodology is expected to be applicable to “discrete events”, to simplify the early adoption of the methodology in any product lifecycle phase. It also facilitates the implementation of the methodology, as it does not require any change to the existing methodologies or organizations, in any company size or market setting.The methodology must support knowledge capture as a “Knowledge-Based Engineering” (KBE) tool, helping in “incremental” methodology development and a continuous improvement flow, and ensuring long-term utilization. It must be suitable for the future implementation of learning, artificial intelligence (AI) or data mining procedures.With these main objectives, the methodology development started with a working principle, integration and schema, as shown in The methodology was first developed to be applied in a competitive and exigent market, such as automotive plastic materials. In detail, the first application is the design review and design optimization of the three main vehicle interior and exterior plastic materials, usually representing the majority (around 58%) of the average vehicle plastic weight , . Some other parts include additional processes, such as thermo negative or slush skin formation, skin wrapping, and polyurethane foaming, as well as system assembly, plastic welding, and gluing. The application of the methodology also makes it possible to integrate actors and expertise from different activities—from vehicle design and product engineering, to process engineering and manufacturing processes expertise, as well purchasing and quality support functions. We also considered the application in different lifecycle phases for different vehicles, business strategies, and optimization targets for each event, allowing us to test and validate the methodology in a wide range of representative situations.According to described aim and objectives, the methodology development started from a previously published basic flowchart , which dThe methodology has a set of tools, as shown on the left side of the schema in 1.Optimization team: The first step is to set up the team who will take part in the optimization process. The best strategy for this is defining a multi-disciplinary team representing all company departments and wide knowledge areas. In our application case, the stable collaboration team was 15 people with profiles covering the main company knowledge areas, cumulating near 300 years of experience; as shown in 2.Knowledge “incremental” database: Once the optimization team has been identified, the first step of the methodology development was to request team members to collect related information, and disseminate it to the rest of the team, including design standards, plastic material information, process guidelines, or regulations to be respected. The “incremental” aim of the methodology enabled us to start applications in real cases, even with “partial” knowledge collection, helping to detect lacking areas and develop a comprehensive knowledge base. As an example, in the first application, we detected a lack of benchmark information, as an interesting optimization opportunity; then, an existing benchmark vehicle database  was incl3.Multi-criteria evaluation set: This is usually defined by the company directors, based on existing key performance indicators (KPIs), and is as complete and stable as possible to allow comprehensive and comparable evaluations. In our case, we used the QCDP set of KPIs , which is well known in the automotive and product development industries ,44. HoweThe multi-criteria evaluation set was placed in the columns, as described in the previous paragraph.A list of “potential design optimization” or “changes” was placed in rows, identified by the optimization team members, based on a related knowledge database and expertise, and ordered considering the origin of the opportunity .The interaction matrix is the central tool of the methodology. It concentrates this information in a profitable format, organizing the following information in a matrix format:After the first application in real cases, the team reviewed and approved the set of evaluation criteria, and also identified “reference members” for the evaluation and continuous improvement of each criterion according to their areas of expertise.This interaction matrix was created in a “collaborative” manner by the optimization team, according to the three steps defined in the methodology and shown in Step 1: Each team member could propose changes in their knowledge or expertise area, mainly based on their experience, obtaining qualitative information and considering the methodology as an effective “knowledge capture” system.Step 2: Every change was evaluated based on its positive or negative impact on every criterion of the multi-criteria evaluation set. The author proposing the change and the reference members had to discuss every impacted criterion to reach a base quantitative value or “score” according to an agreed classification, with values from −5 to +5 , according to Arithmetic means of the answered scores, to allow reference members to evaluate their previous scores and agree to set the answer mean as the resultant score for the impact.Detection of dispersions or lack of stability in answer scores based on normal distribution calculation. In this case, disperse values allowed the team to detect the need for the review of the scores and changes to clarify the origin of these dispersions , better explain them to the team, and then re-review the scores to obtain the agreed resultant score for the dispersive values.Step 3: Once the base value for the impacts had been defined, the entire interaction matrix was evaluated by the entire team, using a Delphi or ETE  methodology, and the group “one-voice” opinion output was set. The Delphi method ,46 is weAfter these three steps, and with all these resultant scores, it was possible to build a reviewed interaction matrix, which was the result of the team’s “one voice” and was useful for application in the following stages. It must be highlighted how easily the process could obtain the “one voice” interaction matrix, based on the experts’ knowledge capture and review strategy.The resultant interaction matrix in our application case is  shown in 2.Business strategy definition: Once the interaction matrix had been defined, the next step of the methodology was the tool that allowed the target of the optimization to be fixed according to the company business strategy. This strategy is usually fixed by the company directors and is frequently different at every moment or project milestone. As an example, in the development phase, the key strategy target could be “respect planning and budget”, and in the serial production phase, the target could be “maximizing cost reduction actions, with as less investment as possible”. This strategy is usually fixed by “verbal” qualitative information, and the key is “translating” this verbal information into parametric and quantitative information.The methodology enabled the “translation” of a “verbal” strategy into a set of quantitative “Targets” and “Restrictions” in the evaluation criteria set defined in 2 emissions or waste volume”.Verbal strategy: “During serial production phase, detect cost reduction actions, with no investment, with application delay less than 1 month, and not affecting negatively lifecycle CO→Target: Detect and order changes by favorable impact in the “Production and Manufacturing Cost Reduction” sub-criteria = (CP) ≤ 1→Applicable in serial phase = (DS) ≥ 1;Investment or entry ticket = (CI) ≤ 1;Impact on delivery time/planning = (DL) ≥ −1;2 emissions = (EC) ≥ 0;Impact on lifecycle COImpact on waste volume = (EW) ≥ 0.Restrictions:Translation into quantitative “Target” and “Restrictions” to criteria set:To explain the “translation” process, the next example is based on a real application case, with a relative complex verbal strategy:With the translation of the strategy into a set of target and restrictions, it was possible to define an algorithm to search the “interaction matrix” and detect and classify the changes that met the defined strategy, as shown below, in pseudocode, with comments after the # symbol.→IF: CP ≤ 1; AND → #verify accomplishment of target.IF: DS = 1; AND → #verify accomplishment of restriction 1.IF CI ≤ 0; AND → #verify accomplishment of restriction 2.IF DL ≥ −1; AND → #verify accomplishment of restriction 3.IF EC ≥ 0; AND → #verify accomplishment of restriction 4.IF EW ≥ 0; THEN → #verify accomplishment of restriction 5.SORT: CP (Max→min) → #classify result according to target.Result = [Interaction Matrix: 1→n]; #run through matrix linesIt is possible to apply this kind of algorithm to any mathematic software working with a matrix or also any database or spreadsheet software that can filter and sort information. In the practical application, the lines of the interaction matrix were verified for “target” and “restrictions”. Lines that did not meet these requirements were rejected. As shown in This procedure result was an ordered list of the best “POTENTIAL Optimizations” in the interaction matrix, which respected the business strategy. This allowed profitable work in the following stages: accelerating design improvement and improving work effectiveness in comparison to existing expert subjective optimization searches; and accelerating changes to meet strategy, market, and customer needs.3.Modeling matrix: Once the “POTENTIAL Optimizations” had been detected and listed according to the strategy, the next step was helping the team to verify if these changes were fully applicable to a real case and helping to perform the robust impact modeling and calculation of the “EXPECTED Impacts”, which enabled the team and management to make Go/No Go decisions around changes based on clear and robust information of the impact calculation in all multi-criteria sets, as shown in This tool enabled the addition and modeling of any subjective origin optimization, including modeling as an additional method to capture knowledge and continuously improve the methodology.4.Checks the verified impacts of every Go decision, in order to detect any deviations in previous stages .Captures any subjective origin actions and checks real results in the same way.Collects and captures any new information used during the process: benchmark good practices, regulation changes, knowledge review proposals, etc.Builds an “Improvement Action List” based on this information.Periodically performs a methodology review with the optimization team to review listed actions and, in our case, correct scores of the Delphi validation, as previously described, and update the knowledge base and methodology tools.Continuous improvement tool: The methodology has an “incremental” orientation, which allows it to be applied from the first stages of the knowledge capture process, but it also needs a tool to ensure continuous improvement. This tool performs the following tasks:These tool and actions ensured the periodical review and optimization of the tools of the methodology as a knowledge capture system, with possible development to some automatic detection of deviations and new information, as well as an artificial intelligence application.5.Phase 1: What to do? Kick-off the event, define the team members, extend team collaborators, and optimize the scope. The company directors provide the business strategy for the event, usually in verbal format.Phase 2: How to do it? The team performs the translation into the quantitative “target” and “Restrictions”, applying it to the most updated interaction matrix, and obtaining the list of potential optimizations. The team adds any additional subjective-origin proposal. The resulting optimization list feeds into the modeling matrix for the event.Phase 3: Why do it? The team collects the information and runs calculations until the modeling matrix is complete with detailed calculations of the expected impacts of the optimization list, providing clear and robust information to help directors make decisions regarding the Go-NoGo of every change.Phase 4: How to do it better? The team tracks the application of Go decisions and calculates the verified impacts once changes are applied. The team compares verified impacts with previous phases of potential and expected impacts, and in the case of deviations, develops an improvement action list. If any other deviation or useful information is found during an event, the action list is also evaluated by the team after every optimization event.Methodology application in discrete events: The steps of a typical application in a discrete optimization event, once the main tools of the methodology have been developed, as shown in As mentioned above, the aim of the methodology is to allow application from early stages, and based on knowledge capture, to perform “incremental” development. In our case, one clear opportunity for the development of the interaction matrix was the integration of historical database information. The team detected available databases regarding product modification and problem-solving events from several different companies, plants, and vehicles. These kinds of databases are useful in our case, as a source of historical information to review the interaction matrix, in particular, to review change impact scores in application delays, cost reduction opportunities, and impacts on quality evaluation criteria. All collected databases used formats and codes based on automotive standards, and were relatively easy to compile; then, the statistical software Minitab v17 application was analyzed as follows:Information from cost reduction actions applied in the period 2019–2021 and derived from 27 different plants worldwide. The database has more than 2400 lines, and 1080 modifications directly related to plastic materials were filtered: type classification, as shown in With his information, a statistical analysis was performed to increase the precision of the interaction matrix impact scores.ANOVA analysis of saving as a quantitative variable versus type as an independent/qualitative variable/factor was conducted to obtain information surrounding the potential of each optimization type, based on statistical confidence intervals. The results are shown in ANOVA 1-factor analysis of delay as a quantitative variable versus type as an independent/qualitative variable/factor was performed to obtain information surrounding the application delays of each optimization type. With results, as shown in A database with approximately 4500 lines for problem solving or QRQC  actions was applied in several different vehicles and companies. Then, 694 actions directly related to vehicle plastic materials were filtered. These actions were also classified considering the type of quality issue according to With this information size, statistical analysis was conducted to review the interaction matrix scores for impacts in duality criteria, as described in the following paragraphs.ANOVA analysis of solving delay as a quantitative variable versus defect type as an independent/qualitative variable/factor was performed in order to detect the root causes with the most complex solution and longer solution delay/impact, and the results are shown in All results of the described historical database analysis were incorporated into the methodology applying the continuous improvement tool, sharing the results with the team to update the interaction matrix tool with this information, and applying it to cells highlighted with blue borders, as well as validating it with an additional Delphi boucle, and the resultant cell values are shown by blue lines in the interaction matrix.It is interesting to highlight that it is still possible to improve the methodology with additional analysis of the existing data, or collecting additional databases from different sources, with the application of “Big Data” principles, or any other information source. The “incremental” aim of the methodology and the continuous improvement tool is to help to capture knowledge benefit from this information. The resultant interaction matrix currently in use is shown in The main objective of the methodology development was to improve the design optimization duties, reduce subjectivity, accelerate optimization, and improve the knowledge capture, ensuring the consideration of the company directors’ business strategy and customer and market demands. The methodology was already applied during 2020 and 2021 in four “Discrete Optimization Events” for three different vehicles of the European market; in three different market segments ; and in different vehicle lifecycle milestones, from the design phase to industrialization and serial production phases, as described in As expected, each optimization event had different scopes and strategies, with different teams . This helped to test the methodology in different scenarios, which is the best way to validate it. The four event strategies and results are listed in detail in In order to analyze the effectiveness of these first methodology application events versus the existing expert team’s subjective optimization research in the same events, a comparison of objective evaluation indicators was performed, as shown in These results confirm the effectiveness of the new methodology in comparison to the existing expert team’s subjective optimization research applied in the same period:Higher successful proposal application ratio.More effective change detection member/workload ratio.Accurately estimated impact modeling, and precise information provided to support management decision making, thus reducing risks.Higher verified results and better workload/results ratio, including the workload for methodology development.The higher success ratio of proposals and better methodology performance in comparison to previously existing subjective-based research are probably due to the innovative business strategy translation into targets and restrictions, which makes it much easier to detect most potential optimizations to be studied, and helps to model the alternatives with detailed impacts in the multi-criteria evaluation set, providing robust information to support decision making. In addition, the robustness of the methodology development, based on knowledge capture and historical data sources, is important.The current limitations of the methodology seem to be related to the historical database used, although the massive data checked only partial interaction matrix scores. It is likely that information will still need to be collected in order to increase statistical analysis and information robustness. Another limitation is related to the continuous improvement. Although we started with a limited knowledge database, which could have affected the results of the first applications, the first utilization of the methodology confirmed its potential for lacking knowledge detection and knowledge capture simplicity, rapidly increasing knowledge robustness, but reducing the effectiveness of the first optimization events.The development of the methodology enabled the collection of useful plastic product and process design-related knowledge that was previously varied and based on subjective experience. Knowledge collection was performed in a “natural” way and in a team workload-efficient manner. The construction of the interaction matrix based on this knowledge and the statistical analysis of historical data, reviewed and validated as the expert team’s “one voice”, provided considerable robustness to ensure confident application in real cases, allowing easier understanding and application and reducing subjectivity, representing a powerful tool to collect company knowledge and accelerate transfer and learning.The application of the methodology in real cases in a market as competitive as automotive plastic materials has also provided good results from the early development stages, allowing the team to carry out “incremental” development, detect more optimization changes, model the impacts accurately and provide precise information for decision making. The defined information structure and continuous methodology improvement strategy also enable long-term updates and utilization. It is important to highlight that it has already been used for more than one and a half years, with several successful reviews and optimization/completion loops.Therefore, it is possible to conclude that the developed methodology demonstrated an advantage in comparison to existing subjective optimization research processes. The team members and directors involved in application have provided favorable opinions regarding the effectiveness and effort–results ratio, the robustness of information during the optimization process and the verified results of the application in real cases.In the near future, the methodology will be applied to additional design optimization events to increase its accuracy and effectivity. The application also allows the methodology and utilization experience to be shared with more teams and stakeholders, as a first step for diffusion into potentially interested departments and stakeholders inside the authors’ companies, who have already confirmed their interest in propagating the utilization of the methodology. The authors are also considering the development of training, support materials, and a comprehensive interface, probably as a web-based application that guides and supports users from stand-alone methodology applications into real cases, helping to expand the application into different plastic markets and companies, which maximizes its competitiveness and sustainability impacts. We also expect to further develop the methodology with continuous improvement strategies via the incorporation of additional information databases, related analysis, and periodical knowledge-based reviews to incorporate any new trend, benchmark solution, process, or material.The wide application of this kind of methodology, which is specifically oriented towards accelerating the product and process design optimization of plastic products, enabling plastic product producers to accelerate this adaptation, is the only way to ensure competitiveness, long-term sustainability, and environmental impact reduction in plastic products.


M = 62.19, SD = 8.24). Participating grandchildren ranged in age from 9 to 12 years old. Focus group transcripts were coded for content related to grandparents’ and grandchildren’s positive behavior changes following the intervention. Findings: Grandparents reported taking more time for themselves, reducing negative self-talk, increasing healthy physical choices, and having better communication skills after participating in the intervention. Similarly, grandchildren reported increased confidence in making friends, making good decisions, and getting along with others. Findings suggest that a self-care and life skills program show promise for improving the health and wellness of grandfamilies.Background: Custodial grandparents experience greater physical health declines and higher rates of depression than their same-age peers who do not provide care, and grandchildren in grandfamilies often have behavior problems. However, few researchers have explored the impact of self-care education on decreasing these negative outcomes. Our study examined how a self-care and life-skills intervention influenced health behavior change in a sample of grandparents and grandchildren. Methods: Data were collected during eleven focus groups (and two interviews) with 55 grandparents, and one focus group with five grandchildren, at 6 months after the 6-week intervention detailed in this paper. Grandparents ranged in age from 46 to 84 years old ( Grandparents raising grandchildren  experience greater physical health declines and higher rates of depression than their age-related peers who are not primary caregivers to grandchildren ,2. The nDespite these challenges and adversities experienced by grandfamilies, grandparents and the grandchildren in their homes are resilient . For exaGrandparents raising grandchildren have been of interest to scholars for the past forty years ,14 and mAs a result of the lack of intergenerational programs and the increased need for programs supporting grandparents and grandchildren, we designed, implemented, and evaluated an innovative intervention to improve grandfamilies’ overall health and wellness through self-care and life skills direct programming. The purpose of this article is to briefly discuss the theoretical underpinnings of the design of the GRANDcares intervention and report findings from separate focus groups with grandparents and grandchildren 6-months after program participation.  and theIn the grandparent portion of the GRANDcares intervention, we made small modifications (with permission) to the Powerful Tools for Caregivers (PTC) program, originally for parents raising children with special needs to render it appropriate for grandparents raising grandchildren (PTC-grandfamilies). The initial PTC program, designed for family caregivers, is highly effective and evidence-based, recognized by the Administration on Aging in 2012 as meeting the highest-level criteria for evidence-based programs. Emphasis is on self-care education, as its taught components are rooted in Bandura’s Social Cognitive Theory. It rests on the assumption that increases in individuals’ self-efficacy will increase the likelihood of the successful performance of tasks . The PTCThe grandchildrens’ program  was created to complement the PTC-grandfamilies program, to support the needs of grandchildren aged 9–12 years. It is delivered at the same time as the grandparent program. Weekly topics and session components are parallel to the PTC-grandfamilies program but are age-appropriate for grandchildren and delivered in an experiential learning setting. The GRANDcares Youth Club is based on 4-H positive youth development theory , which aParticipants in the PTC-grandfamilies and the GRANDcares Youth Club helped us to understand the impacts of these programs on self-care practices and health-related outcomes in grandparents, as well as on life skills and positive behavioral outcomes in grandchildren. The research questions guiding our focus group protocols and data analyses were: (1) What did grandparents and grandchildren learn about self-care and life skills that they continue to use 6 months after the GRANDcares intervention? (2) What individual and family-level protective factors were influenced by the grandfamilies’ participation in the GRANDcares intervention?Focus groups were used to understand participants’ outcomes because: they are useful in gathering data from individuals who have had similar experiences ; are appIn order to participate in the GRANDcares intervention, delivered in the states of Colorado and Hawaii in the United States, adults had to identify as the primary caregiver , with no parent present in the home, for one or more grandchild(ren) under the age of 18 years old. We did not place any exclusion criteria on the length of time that they had been raising grandchildren; however, we strongly encourage any grandparent that had been raising a grandchild for less than 6 months to consider delaying their enrollment. All grandchild participants were between the ages of 9 and 12 years old and were living in grandparent-headed homes. Grandparents and grandchildren who had participated in the GRANDcares intervention took part in one focus group at the 6-month follow-up. All focus groups were conducted by a trained research assistant and lasted approximately 45 min to 1 h. Responses from all groups were audio-recorded and transcribed verbatim. Identical questions and procedures were used in individual interviews with 2 grandparents who did not attend focus group sessions. Including both generations, 11 focus groups and 2 interviews with grandparents, and one focus group with grandchildren were conducted. Participants were prompted to address specific questions see . Due to SD = 8.43, range: 39 to 83 years), raising 243 grandchildren under the age of 18-years-old , completed baseline assessments. Nearly three-quarters, 104 (70%), of the grandparents completed the intervention. At a 6-month follow-up, 55 grandparents (86% grandmothers), ranging in age from 46 to 84 years  and who were raising a total of 83 grandchildren, participated in the focus groups/interviews. One focus group was held for grandchildren, 2 granddaughters and 3 grandsons ranging in age from 9 to 12 years old, participated in this focus group.A total of 149 grandparents, average age 62 years old . Further, in line with our guiding theories and conceptual model (see ), as welThe first theme, grandfamilies’ engagement in physical and leisure activities, was reflected in the grandparents’ descriptions of strategies learned as a result of the program and used to cope during stressful situations. Such activities included building on hobbies such as sewing, and engaging in leisure activities. One grandparent stated, “Mindfulness, you know and digging deeper into that, and with the GRANDcares class the journaling, of listening to music, you know that is calm and soothing”. In addition, grandparents reflected that they learned healthy coping strategies that they could use to manage their stress. For example, grandparents often discussed taking walks, hiking, doing yoga, and having plenty of rest. One grandparent went as far to share that her long-term action plan was to stop smoking. She stated that in the past 6 months, “I also quit smoking. I like, quit smoking”. Grandparents also discussed how other people  supported them in staying physically healthy. For example, one grandparent shared:That young boy is keeping me young. By playing football and come on let’s go. You know he wants me to go to the skate park with him and watch him and I do. And before I wouldn’t do things like that. … Now I feel better. More healthy in my mind. More because I’m stopping to give my time to him and going out and enjoying things like that.The second theme, the grandfamilies’ ability to manage emotional stressors, emerged as several grandparents discussed having hope and a positive outlook on life as they navigated situations perceived as being within their control. Many grandparents discussed how they let go of the need to control the situation, regardless of how it arose. Grandparents often discussed the importance of taking a ‘break’ or finding time to ‘breathe’ to calm themselves. This internal resource is illustrated in one grandparents’ statement, “I take a deep breath, go in my room and close the door and go … [breathes deeply] ‘okay, my room’s okay.’ Shut their door”. Moreover, when another grandparent stated, “The breathing technique. … Just take some deep breathes, leave the room, deep, deep breathes and it just calms me and makes me tackle the next hour, or whatever is going on”. Further, grandparents discussed an increase in self-efficacy. For example, a grandparent stated, “To realize and to depend on myself and not doubt myself as much. I was like ‘you know something you don’t need a college degree to raise a kid’” and another grandparent stated, “I would say, I’m probably stronger than I think and can be resourceful and make things work … strong even when I feel weak”. Further, another grandparent reflected on what had not been working with how she thought about her relationships, family, and control of the situation before the intervention. She stated:I was so fixated on what am I doing wrong. What can I do better? Why aren’t things good. Why is my relationship failing, and when I let go of all that worry and just concentrated on what is and that I can’t change it, I don’t know it was like this thing happened. I was able to say, it’s okay to care for myself. It’s okay to let go. It’s okay to not make things be what you want them to be. Things can be okay without you forcing it.This reflected the ways in which grandparents viewed relationships with their grandchildren and other family members in the context of social support and meaning, illustrating a pattern of wanting to control situations and, because of the class, becoming stronger in emotion-focused coping. For example, one grandparent stated, “Making time for him [grandson]. Making time for the wife and others you know what I mean? It’s not all about me”. It was evident by these grandparents’ reflections that the skills learned during the program were useful to their overall wellness in the face of relationships with other family members.Further, as grandparents discussed their day-to-day experiences raising their grandchildren, they reflected they were better able to manage challenges as a result of their participation in the program. For example, one grandparent stated, “I used to think of life being like a rollercoaster with all its ups and downs and turns and twists and unexpected things, and now I think of it more as a road, and I do have some control”. Another coping strategy that grandparents discussed was learning to set boundaries. One grandparent illustrated this by saying, “Two things [I learned], one is don’t judge what you don’t know. And, the other one that I have been thinking of is ‘not my circus, not my monkeys”.Additionally, grandparents often discussed that, as a result of the class, they are more confident in how they raised their grandchildren. For example, one grandparent stated, “It helped me build [my] own confidence level and [my] own self-esteem. We shared a lot of resources, which helped tremendously. I really loved this class because I know when I came in, I was like shocked still and crying”. Grandparents also discussed the changes they made to their lives as a result of this program and how these changes influenced their grandchildren. For example, one grandparent stated, “I’m more relaxed and that allows them (grandsons) to relax. … They’ve reflected that as well. They’re calmer”. Grandparents also discussed increased awareness, and one grandparent reflected, “[I’m] aware of like their [grandchildren’s] attitudes, their moods, [and] more mindful of what is more important to a healthy relationship with them and not so much yelling”.Grandparents specifically mentioned implementing many of the tools they learned during class. For example, grandparents were taught how to use “I” statements and the importance of being assertive when communicating. Mastery of this skill was evident in the following grandparent statements, “Using “I” statements instead of you has improved our communication a lot” and “I find myself being a little more assertive, um that comes along with the self-care that I seem to be focusing on”. Furthermore, grandparents discussed how these helpful tools translated to better communication with their grandchildren. One grandparent stated, “Its working great cause now my grandson, I can talk to him and he looks at me and he respects what I say”. Another grandparent reflected how the changes she made resulted in her “(grandchildren) coming to me more and talking about … whatever’s bothering them”. Yet, grandparents still struggled with implementing these tools to control their emotions, while at the same time recognizing that it is okay to protect themselves from challenging situations and prevent further emotional challenges. For example, one grandparent stated:I still struggled with the ‘I’ statement with my daughter, mother and granddaughters. She just … she can really piss me off . And I, you know, it’s to the point where she … just her calling me. I don’t even … At times, I don’t just answer the phone. No one talks to her. And I feel, part of me feels bad, you know, this is my daughter. But, if I’m not careful, I know she just sucks the life out of me.These communication skills served grandparents well in the context of managing themselves and connecting with their grandchildren. Many grandparents also reflected that it helped them in other challenging situations with other family members and schoolteachers. This was reflected in the following statement from a grandparent:It has taught me a lot about communication and interaction, resources, and how to deal with members of the family and the school, and other people in general. It’s given me tools to help them [grandchildren] say things to people who might ask them uncomfortable questions.Another grandparent mentioned how this helped improve connections among her granddaughter, her granddaughter’s teacher, and herself when she stated, “It has opened up even more than deeper communication between me and her teacher … and she was hugging her the next day. Using that technique was so, so good”.In addition to grandparents, grandchildren also discussed how the 6-week program impacted their lives. For example, one grandchild stated that the youth club provided a way for her to “learn how to cooperate with each other” and that she thought it was “helpful for real life, teaches [us] how to use different tools and think about different things”. Another grandchild reflected that it supported, “Real life–used tools: [I] used to be really shy,  learned how to talk to other people, [and] now made a lot of friends”. Grandchildren’s reflection of how they took what they learned during the class and applied it to their lives illustrated the applicability of the skills they learned from the intervention.Similar to what grandparents reported, grandchildren also mentioned gaining knowledge of how to manage themselves as well as access support from others. For example, one grandchild stated, “Set goals for ourselves. That was really fun. I still do the goals that I set in class”. Another grandchild reflected that they “trusted everything and everyone”. These grandchildren examples showcased the awareness and use of internal and external resources that they gained as a result of the program.The third theme, the grandfamilies’ establishment of social and community support systems, was illustrated when grandfamilies discussed their flexibility when dealing with challenges and their utilization of social and community resources when they needed them. For example, grandparents discussed using external resources through the local food banks, grandfamily coalitions/support groups, and counseling services. One grandparent stated, “that’s when I started really noticing, ‘oh, maybe you are a little depressed.’ So, I started in therapy”. and another grandparent needed help with cooking and stated, “using more the meal help services” was useful during stressful days. Additionally, many grandparents stated that finding other grandparents in similar situations through this program served as a support mechanism. This was illustrated by one grandparent:The peer support is huge … I didn’t realize until I heard everybody’s story … and a couple of times I thought ‘wow! I’m part of this group now … and I think that’s huge you know. You’re out there and you feel like you’re alone … woe is me [laughs], I give up my life.Moreover, another grandparent stated, “Know[ing] that others have the same issues. I couldn’t believe how similar [her—name of another participant] and I were with a lot of stuff”. Grandparents also shared how raising grandchildren often puts them in situations where they feel out of place, yet they feel connected to others since participating in this intervention. For example, one grandparent stated:I liked just being with other adults who understood what it was like to be a grandparent because when I go to school to pick her up, everybody is in their 30 s with their leggings and being in good shape and here I come going like ‘I don’t fit into this picture.’In addition, grandparents reported how they maintained contact with each other after the program ended. In particular, a few grandparents reflected on this during a focus group. One grandparent said, “you know I’ve connected with some of you outside a little bit and plan to do that more… I hope we keep meeting and do things outside in the moments we can steal”. Another grandparent in the same focus group replied, “[we] get together once a month or we try to. We have a date out there so if you can make it great….but that’s just been nice having, even if we get to see each other once every two months”. Then a third grandparent replied, “I think knowing that I am just part of this whole, …that I’m not alone. There’s a whole bunch of other grandmas out there exhausted trying to take care of their kids and it’s a very noble cause”. Thus, the peer-to-peer support and mentoring may have assisted in grandparents’ ability to further navigate challenging situations.Grandparents whose grandchildren participated in the youth club reported that their grandchildren looked forward to the sessions and excitement in being around children who “are like me” or also part of a grandfamily. Grandchildren who participated in the focus group reflected that they enjoyed being around peers with similar family arrangements. For example, one grandchild stated, “you get to be yourself and get to have a lot of fun!” Further, reflecting the excitement for the program and connections made between grandchildren, another grandchild stated that, “The party was too short at the end [of the program]”.The findings of this study demonstrate that a grandfamily intervention grounded in a strengths-based approach fosters improvements in the self-care practices and life skills of both grandparent and grandchild. Above all, after having participated in the GRANDcares intervention, both generations discussed having learned useful coping strategies and skills that helped them to deal with stressors related to living in skipped-generation households. For example, grandparents discussed having a positive outlook and stronger connections to their grandchildren/other family members during the 6-month focus groups. Both generations reflected upon building problem-solving skills, being resourceful, and finding they had support from their peers , all protective factors for supporting family resiliency .The findings from this study include individual and family-level changes. This is consistent with previous intervention research reporting that grandparents raising grandchildren can: improve their parenting practices ,19; incrThe present study reveals that after participating in the GRANDcares intervention, both grandparents and grandchildren used and implemented skills learned during the program immediately after the program and through the 6-month follow-up. In response to our first research question, we discovered, through the reflections and discussion among grandparents, that changes in self-care and life skills took place among grandfamilies. For example, grandparents spoke about when they face a problem, they are better able to manage it, and they are empowered to take control. These grandparents seemed excited to use the skills they learned during the program to fix or change things, and they discussed how these changes positively influenced themselves and their grandchildren, including those grandchildren that did not participate in the GRANDcares Youth Club. Several grandparents gave examples of how taking breaks when under stress and using calming techniques during emotionally challenging situations not only helped their overall wellness but also provided their grandchildren with role-modeling of positive health behaviors. Grandparents further discussed seeing changes in their grandchildren’s behaviors, such as better listening skills and coping with school or peer-related stress. Grandparents reflected that they believed this was based on what they had learned during the PTC-grandfamilies program; thus, even when grandparents are the target audience for programming, such interventions may also reduce both internal and external challenges of their grandchildren . As a reGrandparents often described how the skills they learned from the intervention translated to their improved communication with their grandchildren, family and friends, their grandchildren’s teachers, and other healthcare and service providers. Trusting other people is not only important for individuals but may also translate to increased communication in families and communities , thus anGrandchildren who participated in the grandchild focus group reflected on what they learned during the GRANDcares Youth Club. They mentioned that they still use action plans to set individual goals and that they learned they could make friends and trust other people. Unlike their grandparents, grandchildren did not discuss strategies when dealing with stressful situations. Grandchildren only reflected on what they learned during the program, what they are still doing, and how they felt interacting with their peers during the program.Many grandfamilies experience challenges that negatively impact their overall health and well-being, as well as threaten opportunities to develop family resiliency ,22. In oWe are cautious in our use of this lens, however, as this theoretical foundation is traditionally used in the context of understanding individuals in the midst of chronic illnesses  and not This study has limitations that should be noted. First, not all grandparents who completed the intervention participated in a 6-month follow-up focus group. These grandparents might have responded differently to the focus group questions and thus, do not represent all participants. Second, grandchildren that participated in the focus group might have been influenced by what they observed their grandparents do or say as a result of their participation in the program. Although grandparents and grandchildren participated in separate focus groups, inherently, they could have influenced each other’s thoughts about the program. Further, perhaps the grandchildren’s framing of the life skills they learned was not because they cannot manage stressful situations, but a result of our grandchildren focus group protocol, which did not prompt the youths to discuss how they apply the skills they learn in everyday situations. Future research may want to use similar but developmentally appropriate protocol questions with both grandparents and grandchildren to further the understanding of how self-care and life skills change as a result of such intervention. Finally, although all cohorts were scheduled to conduct focus groups, due to COVID-19 and subsequent research restrictions during the final three months of the project, not all cohorts of grandparents and grandchildren were given the opportunity to participate in a focus group. New or different findings from the data might have emerged from their experiences with the pandemic and thus are not represented in the coding scheme. As a result, these findings are only representative of the grandfamilies that participated in the focus groups and do not represent all grandparents or grandchildren that completed the 6-week intervention.Findings from this study describe grandparents’ and grandchildren’s implementation of skills following both generations’ participation in educational programming designed to improve their self-care practices and life skills. The findings advance our understanding of how family interventions using resilience and strengths-based approaches may enhance the health and wellness of vulnerable populations. In sum, these findings support calls to advance intergenerational programming supporting grandfamilies, with particular attention to meeting the needs of both grandparents, who are at risk of increased negative outcomes to their physical and mental health, and grandchildren, who are known to experience adverse childhood events and trauma. These multigenerational efforts should include skill-building techniques, group discussion and reflection, and respite opportunities for grandfamilies. With further program development and evaluation, such programming efforts may lead to additional insights into the most effective intergenerational interventions for grandfamilies.