The Mathematics of Relatedness

社会互动对老年人是有益的，无论他们是健康的还是受到退行性疾病的影响。 社会参与不仅带来支持，而且对大脑结构、行为和认知产生影响，从而减缓 衰老。然而，衰老过程产生了多种变化，损害了人们的互动能力 与他人(行动迟缓或身体虚弱，不能经常与家人一起出游；思维过程和语言能力) 流利得太慢，听得太弱，不能保证在集体谈话中足够频繁地轮流交谈 更年轻的人；等等)，导致众多和各种社会关系的损耗。这项研究的目的是 该计划将由社会认知科学家、数学物理学家组成的跨学科团队进行 和老年护理专家，是要了解基本原则的保存或丢失 老龄化中的社会互动。这是通过对社会基础进行数学建模来实现的 在年长和年轻的不同群体中的融合和隔离，并通过开展 记忆与健康中心老年人和年轻人参与集体活动的观察性研究 (讲故事，温柔的瑜伽，音乐制作)。我们的社会协调数学模型(经经验验证 在年轻人中)允许不同的每个代理人的“耦合”能力，(行为或认知)减慢的速度， 记忆过程中的社会适应和行为噪声水平。初步证据表明， 差异和弱耦合导致协调周期更短、频率更低，这从根本上说是 依赖于规模和环境。理论还表明，噪声增强了异质基团的稳定性， 同时倾向于扰乱更同质的那些。所有这些初步发现都指向系统性 效果：互动的机会不仅取决于个人，还取决于比赛或比赛 个人与其社会环境之间的不匹配。因此，这项研究的贡献在于 行为和社会科学中的方法论和衡量方法取决于对此的迫切需要的强调 社会行为的系统性，即整体对局部的作用，这是复杂性的一个关键属性 系统。它导致了量化个人和集体行为的示范性框架；提供 分析策略以表征他们的纠缠；并识别线索以识别何时发生系统性影响 很可能正在发挥作用。这个项目的具体目标是，首先并通过模型，量化社会 环境对老年人社会互动的影响；第二，通过经验观察，发展 将模型的第一原则与经过验证的结果联系起来的翻译工作，以设计社会 最大限度地提高连通性的互动。所有这些进步将有助于维持行为和认知 储备和延长健康和功能衰老的跨度。因为它的基础在总体上 协调的数学模型、研究结果及其方法论也可广泛应用于 翻译背景，包括传染性健康和传染性疾病的许多方面。

Social interactions are beneficial for aging individuals, be they healthy or affected by degenerative disease. Social engagement not only brings support but also acts on brain structure, behavior and cognition to slow aging. The aging process, however, produces multiple changes that compromise people’s ability to interact with others (person too slow or frail to keep to regular outings with family; thought processes and verbal fluency too sluggish, and hearing too feeble, to secure sufficiently frequent turns-at-talk in group conversation with younger individuals; etc.), leading to attrition of numerous and varied social links. The goal of this research program, to be conducted by an interdisciplinary team of socio-cognitive scientists, mathematical physicists and geriatric nursing experts, is to gain understanding on first principles underlying preservation or loss of social interaction in aging. This is accomplished by mathematically modeling the underpinnings of social integration and segregation within heterogeneous groups of older and younger individuals, and by conducting observational studies of group activities involving elderly and younger adults in a memory and wellness center (storytelling, gentle yoga, music making). Our mathematical model of social coordination (empirically validated in young adults) allows to vary each agent’s “coupling” capabilities, (behavioral or cognitive) slowing pace, the memory process of social adaptation and behavioral noise level. Preliminary evidence suggests that pace discrepancy and weak coupling lead to briefer, less frequent periods of coordination, which are fundamentally scale- and context-dependent. Theory also suggests that noise enhances the stability of heterogenous groups, while tending to disrupt that of more homogenous ones. All of those preliminary findings point to systemic effects: interactional opportunities not only depend on individuals, but also nontrivially on the match or mismatch between individuals and their social environment. Therefore, the contribution of this research on methodology and measurement in the behavioral and social sciences lies in a much-needed emphasis on this systemic of social behavior, that is, the effect that the whole exerts on the parts, a key property of complex systems. It leads to an exemplary framework for quantifying individual and collective behavior; provides analysis strategies to characterize their entanglement; and identifies cues to recognize when systemic effects are likely at play. The specific aims of this projects are, first and via models, to quantify the effect that the social environment exerts on elderly social interactions and second, via empirical observations, to develop translational work that connects the model’s first principle with verified outcomes so as to engineer social interactions that maximize connectedness. All of those advances will help to sustain behavioral and cognitive reserve and extend the span of healthy and functional aging. Because of its foundation in a general mathematical model of coordination, the findings and their methodology can also apply in a broad range of translational contexts, including the many facets of communicable health and communicable disease.