The Mathematics of Relatedness

社会交往对老年人是有益的，无论他们是健康的还是受退行性疾病的影响。 社会参与不仅能带来支持，还能影响大脑结构、行为和认知， 衰老然而，衰老过程会产生多种变化，损害人们的互动能力 与其他人（人太慢或虚弱，不能与家人定期外出;思维过程和语言 流利度太慢，听力太弱，无法在小组对话中获得足够频繁的发言机会 年轻人;等等），导致众多和各种各样的社会联系的损耗。本研究的目的 计划，将由社会认知科学家，数学物理学家， 和老年护理专家，是为了了解基本原则的保留或损失， 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 在老年人和年轻人的异质群体中的融合和隔离，并通过开展 在记忆和健康中心对老年人和年轻人进行的群体活动的观察性研究 （讲故事，温和瑜伽，音乐制作）。我们的社会协调数学模型（经验验证 在年轻的成年人）允许改变每个代理的“耦合”能力，（行为或认知）放缓的步伐， 记忆过程的社会适应和行为噪声水平。初步证据显示， 差异和弱耦合导致更短、更不频繁的协调期，从根本上说， 规模和上下文相关。理论还表明，噪音增强了异质群体的稳定性， 同时倾向于破坏更同质的那些。所有这些初步调查结果都表明， 影响：干扰机会不仅取决于个人，而且也不可避免地取决于比赛或 个人与社会环境的不匹配。因此，本研究对 行为科学和社会科学中的方法论和测量方法就在于对这一点的强调 社会行为的系统性，即整体对部分的影响，复杂性的一个关键属性 系统.它为量化个人和集体行为提供了一个示范性的框架; 分析策略，以表征其纠缠;并确定线索，以识别系统性影响时， 很可能在玩。这个项目的具体目标是，首先通过模型，量化社会影响， 环境对老年人社会交往的影响，其次，通过实证观察，发展 翻译工作，将模型的第一原则与验证的结果联系起来，以设计社会 最大化连通性的互动。所有这些进步将有助于维持行为和认知 保留和延长健康和功能性衰老的寿命。因为它的基础是一个 协调的数学模型，研究结果及其方法也可以应用于广泛的 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.