Effects of toe-out and toe-in gaits on lower-extremity kinematics, dynamics, and electromyography

Toe-in and toe-out gait modifications have received increasing attention as an effective, conservative treatment for individuals without severe osteoarthritis because of its potential for improving knee adduction moment (KAM) and knee flexion moment (KFM). Although toe-in and toe-out gaits have positive effects on tibiofemoral (TF) joint pain in the short term, negative impacts on other joints of the lower extremity may arise. The main purpose of this study was to quantitatively compare the effects of foot progression angle (FPA) gait modification with normal walking speeds in healthy individuals on lower-extremity joint, ground reaction force (GRF), muscle electromyography, joint moment, and TF contact force. Experimental measurements using the Vicon system and multi-body dynamics musculoskeletal modelling using OpenSim were conducted in this study. Gait analysis of 12 subjects (n = 12) was conducted with natural gait, toe-in gait, and toe-out gait. One-way repeated measures of ANOVA (p < 0.05) with Tukey’s test was used for statistical analysis. Results showed that the toe-in and toe-out gait modifications decreased the max angle of knee flexion by 8.8 and 12.18 degrees respectively (p < 0.05) and the max angle of hip adduction by 1.28 and 0.99 degrees respectively (p < 0.05) compared to the natural gait. Changes of TF contact forces caused by FPA gait modifications were not statistically significant; however, the effect on KAM and KFM were significant (p < 0.05). KAM or combination of KAM and KFM can be used as surrogate measures for TF medial contact force. Toe-in and toe-out gait modifications could relieve knee joint pain probably due to redistribution of TF contact forces on medial and lateral condylar through changing lateral contact centers and shifting bilateral contact locations

Global Mie Scattering

In various subdisciplines of optics and photonics, Mie theory has been serving as a fundamental language and play indispensable roles widely. Conventional studies related to Mie scattering largely focus on local properties such as differential cross sections and angular polarization distributions. Though spatially integrated features of total cross sections in terms of both scattering and absorption are routine for investigations, they are intrinsically dependent on the specific morphologies of both the scattering bodies and the incident waves, consequently manifesting no sign of global invariance. Here we propose global Mie scattering theory to explore topological invariants for characterizations of scatterings by any obstacles of arbitrarily structured or polarized coherent light. It is revealed that, independent of distributions and interactions among the scattering bodies of arbitrary geometric and optical parameters, in the far field inevitably there are directions where the scatterings are either zero or circularly polarized. Furthermore, for each such singular direction we can assign a half-integer index and the index sum of all those directions are bounded to be a global topological invariant of $2$. The global Mie theory we propose, which is mathematically simple but conceptually penetrating, can render new perspectives for light scattering and topological photonics in both linear and nonlinear regimes, and would potentially shed new light on the scattering of acoustic and matter waves of various forms.Comment: Eight pages and four figures; Comments to welcom

A Network Celebrity Identification and Evaluation Model Based on Hybrid Trust Relation

Trust-based celebrity user identification is the key to the industry\u27s reputation for electronic word of mouth. However, trust and mistrust are independent and coexistent concepts. In this context, we need to consider the existence of the two kinds of user relations brought about by the impact. This paper analyzes the characteristics of trust and distrust in social networks, and gives formal descriptions of trust networks, untrusted networks, and mixed trust networks. Based on the indicators such as degree distribution, correlation coefficient, and matching coefficient, the structural properties of mixed trust networks are studied. Based on the PageRank algorithm, the HTMM metrics affecting users under the mixed trust network environment are proposed. Finally, the validity of HTMM is verified through a real data set containing trust and distrust. Experimental results show that the results of HTMM\u27s celebrity user identification method still have a low level of trust